Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,6,Mod(137,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("138.137");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.1329671342\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 137.10 | ||
Character | \(\chi\) | \(=\) | 138.137 |
Dual form | 138.6.d.a.137.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.00000i | − | 0.707107i | ||||||
\(3\) | −15.1862 | + | 3.51856i | −0.974193 | + | 0.225716i | ||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0.0328033 | 0.000586803 | 0.000293402 | − | 1.00000i | \(-0.499907\pi\) | ||||
0.000293402 | 1.00000i | \(0.499907\pi\) | ||||||||
\(6\) | 14.0742 | + | 60.7447i | 0.159605 | + | 0.688859i | ||||
\(7\) | − | 156.501i | − | 1.20718i | −0.797295 | − | 0.603590i | \(-0.793737\pi\) | ||
0.797295 | − | 0.603590i | \(-0.206263\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | 218.240 | − | 106.867i | 0.898105 | − | 0.439781i | ||||
\(10\) | − | 0.131213i | − | 0.000414933i | ||||||
\(11\) | 514.521 | 1.28210 | 0.641049 | − | 0.767500i | \(-0.278500\pi\) | ||||
0.641049 | + | 0.767500i | \(0.278500\pi\) | |||||||
\(12\) | 242.979 | − | 56.2969i | 0.487097 | − | 0.112858i | ||||
\(13\) | 415.779 | 0.682345 | 0.341172 | − | 0.940001i | \(-0.389176\pi\) | ||||
0.341172 | + | 0.940001i | \(0.389176\pi\) | |||||||
\(14\) | −626.004 | −0.853605 | ||||||||
\(15\) | −0.498157 | + | 0.115420i | −0.000571660 | + | 0.000132451i | ||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1767.95 | −1.48371 | −0.741853 | − | 0.670563i | \(-0.766053\pi\) | ||||
−0.741853 | + | 0.670563i | \(0.766053\pi\) | |||||||
\(18\) | −427.467 | − | 872.958i | −0.310972 | − | 0.635056i | ||||
\(19\) | − | 327.569i | − | 0.208170i | −0.994568 | − | 0.104085i | \(-0.966809\pi\) | ||
0.994568 | − | 0.104085i | \(-0.0331915\pi\) | |||||||
\(20\) | −0.524853 | −0.000293402 | ||||||||
\(21\) | 550.657 | + | 2376.65i | 0.272479 | + | 1.17603i | ||||
\(22\) | − | 2058.08i | − | 0.906580i | ||||||
\(23\) | 1263.99 | − | 2199.70i | 0.498223 | − | 0.867049i | ||||
\(24\) | −225.188 | − | 971.915i | −0.0798025 | − | 0.344429i | ||||
\(25\) | −3125.00 | −1.00000 | ||||||||
\(26\) | − | 1663.11i | − | 0.482491i | ||||||
\(27\) | −2938.21 | + | 2390.79i | −0.775662 | + | 0.631148i | ||||
\(28\) | 2504.01i | 0.603590i | ||||||||
\(29\) | − | 1444.40i | − | 0.318928i | −0.987204 | − | 0.159464i | \(-0.949023\pi\) | ||
0.987204 | − | 0.159464i | \(-0.0509766\pi\) | |||||||
\(30\) | 0.461681 | + | 1.99263i | 9.36568e−5 | + | 0.000404225i | ||||
\(31\) | −8826.33 | −1.64959 | −0.824795 | − | 0.565432i | \(-0.808710\pi\) | ||||
−0.824795 | + | 0.565432i | \(0.808710\pi\) | |||||||
\(32\) | − | 1024.00i | − | 0.176777i | ||||||
\(33\) | −7813.60 | + | 1810.37i | −1.24901 | + | 0.289389i | ||||
\(34\) | 7071.80i | 1.04914i | ||||||||
\(35\) | − | 5.13375i | − | 0.000708377i | ||||||
\(36\) | −3491.83 | + | 1709.87i | −0.449052 | + | 0.219891i | ||||
\(37\) | 1692.05i | 0.203193i | 0.994826 | + | 0.101597i | \(0.0323951\pi\) | ||||
−0.994826 | + | 0.101597i | \(0.967605\pi\) | |||||||
\(38\) | −1310.28 | −0.147199 | ||||||||
\(39\) | −6314.09 | + | 1462.94i | −0.664736 | + | 0.154016i | ||||
\(40\) | 2.09941i | 0.000207466i | ||||||||
\(41\) | − | 12287.7i | − | 1.14159i | −0.821093 | − | 0.570795i | \(-0.806635\pi\) | ||
0.821093 | − | 0.570795i | \(-0.193365\pi\) | |||||||
\(42\) | 9506.60 | − | 2202.63i | 0.831576 | − | 0.192672i | ||||
\(43\) | 21379.8i | 1.76332i | 0.471881 | + | 0.881662i | \(0.343575\pi\) | ||||
−0.471881 | + | 0.881662i | \(0.656425\pi\) | |||||||
\(44\) | −8232.33 | −0.641049 | ||||||||
\(45\) | 7.15898 | − | 3.50559i | 0.000527011 | − | 0.000258065i | ||||
\(46\) | −8798.79 | − | 5055.96i | −0.613096 | − | 0.352297i | ||||
\(47\) | 972.502i | 0.0642164i | 0.999484 | + | 0.0321082i | \(0.0102221\pi\) | ||||
−0.999484 | + | 0.0321082i | \(0.989778\pi\) | |||||||
\(48\) | −3887.66 | + | 900.751i | −0.243548 | + | 0.0564289i | ||||
\(49\) | −7685.53 | −0.457282 | ||||||||
\(50\) | 12500.0i | 0.707107i | ||||||||
\(51\) | 26848.4 | − | 6220.64i | 1.44542 | − | 0.334896i | ||||
\(52\) | −6652.46 | −0.341172 | ||||||||
\(53\) | −16242.2 | −0.794246 | −0.397123 | − | 0.917765i | \(-0.629991\pi\) | ||||
−0.397123 | + | 0.917765i | \(0.629991\pi\) | |||||||
\(54\) | 9563.14 | + | 11752.8i | 0.446289 | + | 0.548476i | ||||
\(55\) | 16.8780 | 0.000752339 | ||||||||
\(56\) | 10016.1 | 0.426802 | ||||||||
\(57\) | 1152.57 | + | 4974.52i | 0.0469873 | + | 0.202798i | ||||
\(58\) | −5777.60 | −0.225516 | ||||||||
\(59\) | − | 7885.38i | − | 0.294912i | −0.989069 | − | 0.147456i | \(-0.952892\pi\) | ||
0.989069 | − | 0.147456i | \(-0.0471085\pi\) | |||||||
\(60\) | 7.97051 | − | 1.84673i | 0.000285830 | − | 6.62253e-5i | ||||
\(61\) | − | 33942.2i | − | 1.16792i | −0.811781 | − | 0.583962i | \(-0.801502\pi\) | ||
0.811781 | − | 0.583962i | \(-0.198498\pi\) | |||||||
\(62\) | 35305.3i | 1.16644i | ||||||||
\(63\) | −16724.8 | − | 34154.7i | −0.530895 | − | 1.08417i | ||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 13.6389 | 0.000400402 | ||||||||
\(66\) | 7241.48 | + | 31254.4i | 0.204629 | + | 0.883184i | ||||
\(67\) | 66229.6i | 1.80246i | 0.433345 | + | 0.901228i | \(0.357333\pi\) | ||||
−0.433345 | + | 0.901228i | \(0.642667\pi\) | |||||||
\(68\) | 28287.2 | 0.741853 | ||||||||
\(69\) | −11455.4 | + | 37852.4i | −0.289659 | + | 0.957130i | ||||
\(70\) | −20.5350 | −0.000500898 | ||||||||
\(71\) | − | 44256.3i | − | 1.04191i | −0.853585 | − | 0.520953i | \(-0.825577\pi\) | ||
0.853585 | − | 0.520953i | \(-0.174423\pi\) | |||||||
\(72\) | 6839.48 | + | 13967.3i | 0.155486 | + | 0.317528i | ||||
\(73\) | −36769.5 | −0.807571 | −0.403786 | − | 0.914854i | \(-0.632306\pi\) | ||||
−0.403786 | + | 0.914854i | \(0.632306\pi\) | |||||||
\(74\) | 6768.20 | 0.143679 | ||||||||
\(75\) | 47456.8 | − | 10995.5i | 0.974193 | − | 0.225716i | ||||
\(76\) | 5241.11i | 0.104085i | ||||||||
\(77\) | − | 80522.9i | − | 1.54772i | ||||||
\(78\) | 5851.76 | + | 25256.3i | 0.108906 | + | 0.470039i | ||||
\(79\) | − | 19660.7i | − | 0.354430i | −0.984172 | − | 0.177215i | \(-0.943291\pi\) | ||
0.984172 | − | 0.177215i | \(-0.0567088\pi\) | |||||||
\(80\) | 8.39765 | 0.000146701 | ||||||||
\(81\) | 36208.0 | − | 46645.1i | 0.613185 | − | 0.789939i | ||||
\(82\) | −49150.7 | −0.807226 | ||||||||
\(83\) | −65271.3 | −1.03998 | −0.519992 | − | 0.854171i | \(-0.674065\pi\) | ||||
−0.519992 | + | 0.854171i | \(0.674065\pi\) | |||||||
\(84\) | −8810.52 | − | 38026.4i | −0.136240 | − | 0.588013i | ||||
\(85\) | −57.9946 | −0.000870644 | ||||||||
\(86\) | 85519.1 | 1.24686 | ||||||||
\(87\) | 5082.21 | + | 21934.9i | 0.0719870 | + | 0.310697i | ||||
\(88\) | 32929.3i | 0.453290i | ||||||||
\(89\) | −116522. | −1.55931 | −0.779655 | − | 0.626209i | \(-0.784606\pi\) | ||||
−0.779655 | + | 0.626209i | \(0.784606\pi\) | |||||||
\(90\) | −14.0223 | − | 28.6359i | −0.000182480 | − | 0.000372653i | ||||
\(91\) | − | 65069.7i | − | 0.823712i | ||||||
\(92\) | −20223.8 | + | 35195.2i | −0.249112 | + | 0.433524i | ||||
\(93\) | 134038. | − | 31056.0i | 1.60702 | − | 0.372338i | ||||
\(94\) | 3890.01 | 0.0454079 | ||||||||
\(95\) | − | 10.7454i | − | 0.000122155i | ||||||
\(96\) | 3603.00 | + | 15550.6i | 0.0399013 | + | 0.172215i | ||||
\(97\) | − | 126143.i | − | 1.36124i | −0.732638 | − | 0.680618i | \(-0.761711\pi\) | ||
0.732638 | − | 0.680618i | \(-0.238289\pi\) | |||||||
\(98\) | 30742.1i | 0.323347i | ||||||||
\(99\) | 112289. | − | 54985.2i | 1.15146 | − | 0.563842i | ||||
\(100\) | 50000.0 | 0.500000 | ||||||||
\(101\) | − | 131351.i | − | 1.28124i | −0.767858 | − | 0.640621i | \(-0.778677\pi\) | ||
0.767858 | − | 0.640621i | \(-0.221323\pi\) | |||||||
\(102\) | −24882.5 | − | 107394.i | −0.236807 | − | 1.02206i | ||||
\(103\) | 61325.3i | 0.569569i | 0.958592 | + | 0.284785i | \(0.0919220\pi\) | ||||
−0.958592 | + | 0.284785i | \(0.908078\pi\) | |||||||
\(104\) | 26609.8i | 0.241245i | ||||||||
\(105\) | 18.0634 | + | 77.9620i | 0.000159892 | + | 0.000690096i | ||||
\(106\) | 64968.7i | 0.561616i | ||||||||
\(107\) | −85774.2 | −0.724264 | −0.362132 | − | 0.932127i | \(-0.617951\pi\) | ||||
−0.362132 | + | 0.932127i | \(0.617951\pi\) | |||||||
\(108\) | 47011.3 | − | 38252.6i | 0.387831 | − | 0.315574i | ||||
\(109\) | 177193.i | 1.42850i | 0.699889 | + | 0.714251i | \(0.253233\pi\) | ||||
−0.699889 | + | 0.714251i | \(0.746767\pi\) | |||||||
\(110\) | − | 67.5119i | − | 0.000531984i | ||||||
\(111\) | −5953.57 | − | 25695.8i | −0.0458638 | − | 0.197949i | ||||
\(112\) | − | 40064.2i | − | 0.301795i | ||||||
\(113\) | 250367. | 1.84451 | 0.922255 | − | 0.386583i | \(-0.126345\pi\) | ||||
0.922255 | + | 0.386583i | \(0.126345\pi\) | |||||||
\(114\) | 19898.1 | − | 4610.28i | 0.143400 | − | 0.0332250i | ||||
\(115\) | 41.4630 | − | 72.1574i | 0.000292359 | − | 0.000508787i | ||||
\(116\) | 23110.4i | 0.159464i | ||||||||
\(117\) | 90739.3 | − | 44432.9i | 0.612817 | − | 0.300082i | ||||
\(118\) | −31541.5 | −0.208534 | ||||||||
\(119\) | 276686.i | 1.79110i | ||||||||
\(120\) | −7.38690 | − | 31.8820i | −4.68284e−5 | − | 0.000202112i | ||||
\(121\) | 103680. | 0.643774 | ||||||||
\(122\) | −135769. | −0.825848 | ||||||||
\(123\) | 43234.9 | + | 186603.i | 0.257675 | + | 1.11213i | ||||
\(124\) | 141221. | 0.824795 | ||||||||
\(125\) | −205.021 | −0.00117361 | ||||||||
\(126\) | −136619. | + | 66899.0i | −0.766626 | + | 0.375399i | ||||
\(127\) | −6066.05 | −0.0333731 | −0.0166866 | − | 0.999861i | \(-0.505312\pi\) | ||||
−0.0166866 | + | 0.999861i | \(0.505312\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | −75226.0 | − | 324677.i | −0.398010 | − | 1.71782i | ||||
\(130\) | − | 54.5557i | − | 0.000283127i | ||||||
\(131\) | 20196.3i | 0.102824i | 0.998678 | + | 0.0514118i | \(0.0163721\pi\) | ||||
−0.998678 | + | 0.0514118i | \(0.983628\pi\) | |||||||
\(132\) | 125018. | − | 28965.9i | 0.624505 | − | 0.144695i | ||||
\(133\) | −51264.9 | −0.251299 | ||||||||
\(134\) | 264918. | 1.27453 | ||||||||
\(135\) | −96.3828 | + | 78.4257i | −0.000455161 | + | 0.000370360i | ||||
\(136\) | − | 113149.i | − | 0.524569i | ||||||
\(137\) | −44141.1 | −0.200929 | −0.100464 | − | 0.994941i | \(-0.532033\pi\) | ||||
−0.100464 | + | 0.994941i | \(0.532033\pi\) | |||||||
\(138\) | 151410. | + | 45821.6i | 0.676793 | + | 0.204820i | ||||
\(139\) | 39732.6 | 0.174426 | 0.0872128 | − | 0.996190i | \(-0.472204\pi\) | ||||
0.0872128 | + | 0.996190i | \(0.472204\pi\) | |||||||
\(140\) | 82.1400i | 0.000354188i | ||||||||
\(141\) | −3421.81 | − | 14768.6i | −0.0144946 | − | 0.0625592i | ||||
\(142\) | −177025. | −0.736739 | ||||||||
\(143\) | 213927. | 0.874832 | ||||||||
\(144\) | 55869.3 | − | 27357.9i | 0.224526 | − | 0.109945i | ||||
\(145\) | − | 47.3811i | − | 0.000187148i | ||||||
\(146\) | 147078.i | 0.571039i | ||||||||
\(147\) | 116714. | − | 27042.0i | 0.445481 | − | 0.103216i | ||||
\(148\) | − | 27072.8i | − | 0.101597i | ||||||
\(149\) | 134915. | 0.497847 | 0.248923 | − | 0.968523i | \(-0.419923\pi\) | ||||
0.248923 | + | 0.968523i | \(0.419923\pi\) | |||||||
\(150\) | −43982.0 | − | 189827.i | −0.159605 | − | 0.688858i | ||||
\(151\) | −497213. | −1.77460 | −0.887299 | − | 0.461195i | \(-0.847421\pi\) | ||||
−0.887299 | + | 0.461195i | \(0.847421\pi\) | |||||||
\(152\) | 20964.4 | 0.0735994 | ||||||||
\(153\) | −385837. | + | 188935.i | −1.33252 | + | 0.652506i | ||||
\(154\) | −322092. | −1.09440 | ||||||||
\(155\) | −289.533 | −0.000967985 | ||||||||
\(156\) | 101025. | − | 23407.1i | 0.332368 | − | 0.0770079i | ||||
\(157\) | 407744.i | 1.32020i | 0.751179 | + | 0.660098i | \(0.229485\pi\) | ||||
−0.751179 | + | 0.660098i | \(0.770515\pi\) | |||||||
\(158\) | −78642.6 | −0.250620 | ||||||||
\(159\) | 246657. | − | 57149.1i | 0.773749 | − | 0.179274i | ||||
\(160\) | − | 33.5906i | − | 0.000103733i | ||||||
\(161\) | −344255. | − | 197815.i | −1.04668 | − | 0.601445i | ||||
\(162\) | −186581. | − | 144832.i | −0.558571 | − | 0.433587i | ||||
\(163\) | −168675. | −0.497259 | −0.248630 | − | 0.968599i | \(-0.579980\pi\) | ||||
−0.248630 | + | 0.968599i | \(0.579980\pi\) | |||||||
\(164\) | 196603.i | 0.570795i | ||||||||
\(165\) | −256.312 | + | 59.3861i | −0.000732924 | + | 0.000169815i | ||||
\(166\) | 261085.i | 0.735380i | ||||||||
\(167\) | 421063.i | 1.16830i | 0.811644 | + | 0.584152i | \(0.198573\pi\) | ||||
−0.811644 | + | 0.584152i | \(0.801427\pi\) | |||||||
\(168\) | −152106. | + | 35242.1i | −0.415788 | + | 0.0963359i | ||||
\(169\) | −198421. | −0.534406 | ||||||||
\(170\) | 231.978i | 0.000615638i | ||||||||
\(171\) | −35006.3 | − | 71488.5i | −0.0915494 | − | 0.186959i | ||||
\(172\) | − | 342077.i | − | 0.881662i | ||||||
\(173\) | − | 488824.i | − | 1.24176i | −0.783906 | − | 0.620880i | \(-0.786775\pi\) | ||
0.783906 | − | 0.620880i | \(-0.213225\pi\) | |||||||
\(174\) | 87739.6 | − | 20328.8i | 0.219696 | − | 0.0509025i | ||||
\(175\) | 489065.i | 1.20718i | ||||||||
\(176\) | 131717. | 0.320524 | ||||||||
\(177\) | 27745.2 | + | 119749.i | 0.0665663 | + | 0.287301i | ||||
\(178\) | 466088.i | 1.10260i | ||||||||
\(179\) | − | 14603.8i | − | 0.0340669i | −0.999855 | − | 0.0170335i | \(-0.994578\pi\) | ||
0.999855 | − | 0.0170335i | \(-0.00542218\pi\) | |||||||
\(180\) | −114.544 | + | 56.0894i | −0.000263506 | + | 0.000129033i | ||||
\(181\) | − | 558410.i | − | 1.26694i | −0.773767 | − | 0.633471i | \(-0.781630\pi\) | ||
0.773767 | − | 0.633471i | \(-0.218370\pi\) | |||||||
\(182\) | −260279. | −0.582453 | ||||||||
\(183\) | 119427. | + | 515451.i | 0.263619 | + | 1.13778i | ||||
\(184\) | 140781. | + | 80895.3i | 0.306548 | + | 0.176148i | ||||
\(185\) | 55.5048i | 0.000119234i | ||||||||
\(186\) | −124224. | − | 536153.i | −0.263283 | − | 1.13633i | ||||
\(187\) | −909647. | −1.90226 | ||||||||
\(188\) | − | 15560.0i | − | 0.0321082i | ||||||
\(189\) | 374160. | + | 459832.i | 0.761909 | + | 0.936363i | ||||
\(190\) | −42.9814 | −8.63767e−5 | ||||||||
\(191\) | 10405.4 | 0.0206383 | 0.0103192 | − | 0.999947i | \(-0.496715\pi\) | ||||
0.0103192 | + | 0.999947i | \(0.496715\pi\) | |||||||
\(192\) | 62202.6 | − | 14412.0i | 0.121774 | − | 0.0282144i | ||||
\(193\) | −300737. | −0.581156 | −0.290578 | − | 0.956851i | \(-0.593848\pi\) | ||||
−0.290578 | + | 0.956851i | \(0.593848\pi\) | |||||||
\(194\) | −504572. | −0.962540 | ||||||||
\(195\) | −207.123 | + | 47.9893i | −0.000390069 | + | 9.03770e-5i | ||||
\(196\) | 122968. | 0.228641 | ||||||||
\(197\) | − | 589962.i | − | 1.08308i | −0.840676 | − | 0.541538i | \(-0.817842\pi\) | ||
0.840676 | − | 0.541538i | \(-0.182158\pi\) | |||||||
\(198\) | −219941. | − | 449155.i | −0.398697 | − | 0.814204i | ||||
\(199\) | − | 77744.8i | − | 0.139168i | −0.997576 | − | 0.0695838i | \(-0.977833\pi\) | ||
0.997576 | − | 0.0695838i | \(-0.0221671\pi\) | |||||||
\(200\) | − | 200000.i | − | 0.353553i | ||||||
\(201\) | −233032. | − | 1.00577e6i | −0.406843 | − | 1.75594i | ||||
\(202\) | −525405. | −0.905974 | ||||||||
\(203\) | −226050. | −0.385003 | ||||||||
\(204\) | −429574. | + | 99530.2i | −0.722708 | + | 0.167448i | ||||
\(205\) | − | 403.077i | − | 0.000669889i | ||||||
\(206\) | 245301. | 0.402746 | ||||||||
\(207\) | 40777.6 | − | 615140.i | 0.0661448 | − | 0.997810i | ||||
\(208\) | 106439. | 0.170586 | ||||||||
\(209\) | − | 168541.i | − | 0.266895i | ||||||
\(210\) | 311.848 | − | 72.2535i | 0.000487972 | − | 0.000113061i | ||||
\(211\) | 408048. | 0.630965 | 0.315482 | − | 0.948931i | \(-0.397834\pi\) | ||||
0.315482 | + | 0.948931i | \(0.397834\pi\) | |||||||
\(212\) | 259875. | 0.397123 | ||||||||
\(213\) | 155718. | + | 672083.i | 0.235175 | + | 1.01502i | ||||
\(214\) | 343097.i | 0.512132i | ||||||||
\(215\) | 701.328i | 0.00103472i | ||||||||
\(216\) | −153010. | − | 188045.i | −0.223145 | − | 0.274238i | ||||
\(217\) | 1.38133e6i | 1.99135i | ||||||||
\(218\) | 708773. | 1.01010 | ||||||||
\(219\) | 558388. | − | 129376.i | 0.786731 | − | 0.182281i | ||||
\(220\) | −270.048 | −0.000376170 | ||||||||
\(221\) | −735076. | −1.01240 | ||||||||
\(222\) | −102783. | + | 23814.3i | −0.139971 | + | 0.0324306i | ||||
\(223\) | 973166. | 1.31046 | 0.655231 | − | 0.755428i | \(-0.272571\pi\) | ||||
0.655231 | + | 0.755428i | \(0.272571\pi\) | |||||||
\(224\) | −160257. | −0.213401 | ||||||||
\(225\) | −681998. | + | 333959.i | −0.898105 | + | 0.439781i | ||||
\(226\) | − | 1.00147e6i | − | 1.30427i | ||||||
\(227\) | 819626. | 1.05573 | 0.527863 | − | 0.849330i | \(-0.322994\pi\) | ||||
0.527863 | + | 0.849330i | \(0.322994\pi\) | |||||||
\(228\) | −18441.1 | − | 79592.3i | −0.0234937 | − | 0.101399i | ||||
\(229\) | − | 633956.i | − | 0.798860i | −0.916764 | − | 0.399430i | \(-0.869208\pi\) | ||
0.916764 | − | 0.399430i | \(-0.130792\pi\) | |||||||
\(230\) | −288.630 | − | 165.852i | −0.000359767 | − | 0.000206729i | ||||
\(231\) | 283325. | + | 1.22284e6i | 0.349345 | + | 1.50778i | ||||
\(232\) | 92441.6 | 0.112758 | ||||||||
\(233\) | 1.30840e6i | 1.57888i | 0.613825 | + | 0.789442i | \(0.289630\pi\) | ||||
−0.613825 | + | 0.789442i | \(0.710370\pi\) | |||||||
\(234\) | −177732. | − | 362957.i | −0.212190 | − | 0.433327i | ||||
\(235\) | 31.9013i | 3.76824e-5i | ||||||||
\(236\) | 126166.i | 0.147456i | ||||||||
\(237\) | 69177.1 | + | 298570.i | 0.0800003 | + | 0.345283i | ||||
\(238\) | 1.10674e6 | 1.26650 | ||||||||
\(239\) | 403526.i | 0.456959i | 0.973549 | + | 0.228479i | \(0.0733754\pi\) | ||||
−0.973549 | + | 0.228479i | \(0.926625\pi\) | |||||||
\(240\) | −127.528 | + | 29.5476i | −0.000142915 | + | 3.31127e-5i | ||||
\(241\) | − | 63519.3i | − | 0.0704470i | −0.999379 | − | 0.0352235i | \(-0.988786\pi\) | ||
0.999379 | − | 0.0352235i | \(-0.0112143\pi\) | |||||||
\(242\) | − | 414722.i | − | 0.455217i | ||||||
\(243\) | −385737. | + | 835761.i | −0.419059 | + | 0.907959i | ||||
\(244\) | 543075.i | 0.583962i | ||||||||
\(245\) | −252.111 | −0.000268334 | ||||||||
\(246\) | 746411. | − | 172940.i | 0.786394 | − | 0.182204i | ||||
\(247\) | − | 136196.i | − | 0.142044i | ||||||
\(248\) | − | 564885.i | − | 0.583218i | ||||||
\(249\) | 991221. | − | 229661.i | 1.01315 | − | 0.234741i | ||||
\(250\) | 820.083i | 0.000829865i | ||||||||
\(251\) | 252393. | 0.252867 | 0.126434 | − | 0.991975i | \(-0.459647\pi\) | ||||
0.126434 | + | 0.991975i | \(0.459647\pi\) | |||||||
\(252\) | 267596. | + | 546475.i | 0.265447 | + | 0.542087i | ||||
\(253\) | 650349. | − | 1.13179e6i | 0.638771 | − | 1.11164i | ||||
\(254\) | 24264.2i | 0.0235983i | ||||||||
\(255\) | 880.716 | − | 204.057i | 0.000848175 | − | 0.000196518i | ||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 708073.i | 0.668722i | 0.942445 | + | 0.334361i | \(0.108520\pi\) | ||||
−0.942445 | + | 0.334361i | \(0.891480\pi\) | |||||||
\(258\) | −1.29871e6 | + | 300904.i | −1.21468 | + | 0.281435i | ||||
\(259\) | 264807. | 0.245290 | ||||||||
\(260\) | −218.223 | −0.000200201 | ||||||||
\(261\) | −154358. | − | 315225.i | −0.140258 | − | 0.286431i | ||||
\(262\) | 80785.1 | 0.0727073 | ||||||||
\(263\) | 809213. | 0.721396 | 0.360698 | − | 0.932683i | \(-0.382539\pi\) | ||||
0.360698 | + | 0.932683i | \(0.382539\pi\) | |||||||
\(264\) | −115864. | − | 500070.i | −0.102315 | − | 0.441592i | ||||
\(265\) | −532.797 | −0.000466066 | ||||||||
\(266\) | 205059.i | 0.177695i | ||||||||
\(267\) | 1.76952e6 | − | 409989.i | 1.51907 | − | 0.351961i | ||||
\(268\) | − | 1.05967e6i | − | 0.901228i | ||||||
\(269\) | − | 1.58306e6i | − | 1.33388i | −0.745110 | − | 0.666941i | \(-0.767603\pi\) | ||
0.745110 | − | 0.666941i | \(-0.232397\pi\) | |||||||
\(270\) | 313.703 | + | 385.531i | 0.000261884 | + | 0.000321848i | ||||
\(271\) | 725411. | 0.600013 | 0.300007 | − | 0.953937i | \(-0.403011\pi\) | ||||
0.300007 | + | 0.953937i | \(0.403011\pi\) | |||||||
\(272\) | −452595. | −0.370926 | ||||||||
\(273\) | 228952. | + | 988160.i | 0.185925 | + | 0.802455i | ||||
\(274\) | 176564.i | 0.142078i | ||||||||
\(275\) | −1.60788e6 | −1.28210 | ||||||||
\(276\) | 183286. | − | 605639.i | 0.144830 | − | 0.478565i | ||||
\(277\) | −959637. | −0.751463 | −0.375732 | − | 0.926729i | \(-0.622609\pi\) | ||||
−0.375732 | + | 0.926729i | \(0.622609\pi\) | |||||||
\(278\) | − | 158930.i | − | 0.123337i | ||||||
\(279\) | −1.92625e6 | + | 943242.i | −1.48151 | + | 0.725459i | ||||
\(280\) | 328.560 | 0.000250449 | ||||||||
\(281\) | −1.23577e6 | −0.933626 | −0.466813 | − | 0.884356i | \(-0.654598\pi\) | ||||
−0.466813 | + | 0.884356i | \(0.654598\pi\) | |||||||
\(282\) | −59074.3 | + | 13687.2i | −0.0442360 | + | 0.0102493i | ||||
\(283\) | − | 2.14356e6i | − | 1.59100i | −0.605956 | − | 0.795498i | \(-0.707209\pi\) | ||
0.605956 | − | 0.795498i | \(-0.292791\pi\) | |||||||
\(284\) | 708100.i | 0.520953i | ||||||||
\(285\) | 37.8081 | + | 163.181i | 2.75723e−5 | + | 0.000119003i | ||||
\(286\) | − | 855707.i | − | 0.618600i | ||||||
\(287\) | −1.92303e6 | −1.37810 | ||||||||
\(288\) | −109432. | − | 223477.i | −0.0777431 | − | 0.158764i | ||||
\(289\) | 1.70579e6 | 1.20138 | ||||||||
\(290\) | −189.524 | −0.000132334 | ||||||||
\(291\) | 443841. | + | 1.91563e6i | 0.307252 | + | 1.32611i | ||||
\(292\) | 588312. | 0.403786 | ||||||||
\(293\) | 2.46156e6 | 1.67510 | 0.837550 | − | 0.546361i | \(-0.183987\pi\) | ||||
0.837550 | + | 0.546361i | \(0.183987\pi\) | |||||||
\(294\) | −108168. | − | 466855.i | −0.0729844 | − | 0.315002i | ||||
\(295\) | − | 258.667i | − | 0.000173055i | ||||||
\(296\) | −108291. | −0.0718396 | ||||||||
\(297\) | −1.51177e6 | + | 1.23011e6i | −0.994475 | + | 0.809193i | ||||
\(298\) | − | 539661.i | − | 0.352031i | ||||||
\(299\) | 525540. | − | 914588.i | 0.339960 | − | 0.591626i | ||||
\(300\) | −759308. | + | 175928.i | −0.487096 | + | 0.112858i | ||||
\(301\) | 3.34596e6 | 2.12865 | ||||||||
\(302\) | 1.98885e6i | 1.25483i | ||||||||
\(303\) | 462167. | + | 1.99472e6i | 0.289196 | + | 1.24818i | ||||
\(304\) | − | 83857.7i | − | 0.0520426i | ||||||
\(305\) | − | 1113.42i | − | 0.000685342i | ||||||
\(306\) | 755741. | + | 1.54335e6i | 0.461391 | + | 0.942236i | ||||
\(307\) | 600443. | 0.363602 | 0.181801 | − | 0.983335i | \(-0.441807\pi\) | ||||
0.181801 | + | 0.983335i | \(0.441807\pi\) | |||||||
\(308\) | 1.28837e6i | 0.773861i | ||||||||
\(309\) | −215776. | − | 931296.i | −0.128561 | − | 0.554870i | ||||
\(310\) | 1158.13i | 0.000684469i | ||||||||
\(311\) | − | 3.09189e6i | − | 1.81269i | −0.422541 | − | 0.906344i | \(-0.638862\pi\) | ||
0.422541 | − | 0.906344i | \(-0.361138\pi\) | |||||||
\(312\) | −93628.2 | − | 404101.i | −0.0544528 | − | 0.235020i | ||||
\(313\) | 842295.i | 0.485963i | 0.970031 | + | 0.242982i | \(0.0781255\pi\) | ||||
−0.970031 | + | 0.242982i | \(0.921875\pi\) | |||||||
\(314\) | 1.63098e6 | 0.933520 | ||||||||
\(315\) | −548.627 | − | 1120.39i | −0.000311531 | − | 0.000636197i | ||||
\(316\) | 314570.i | 0.177215i | ||||||||
\(317\) | − | 3.07049e6i | − | 1.71616i | −0.513512 | − | 0.858082i | \(-0.671656\pi\) | ||
0.513512 | − | 0.858082i | \(-0.328344\pi\) | |||||||
\(318\) | −228596. | − | 986626.i | −0.126766 | − | 0.547123i | ||||
\(319\) | − | 743174.i | − | 0.408897i | ||||||
\(320\) | −134.362 | −7.33504e−5 | ||||||||
\(321\) | 1.30258e6 | − | 301801.i | 0.705573 | − | 0.163478i | ||||
\(322\) | −791262. | + | 1.37702e6i | −0.425285 | + | 0.740117i | ||||
\(323\) | 579126.i | 0.308864i | ||||||||
\(324\) | −579327. | + | 746322.i | −0.306593 | + | 0.394970i | ||||
\(325\) | −1.29931e6 | −0.682344 | ||||||||
\(326\) | 674702.i | 0.351615i | ||||||||
\(327\) | −623465. | − | 2.69089e6i | −0.322435 | − | 1.39164i | ||||
\(328\) | 786412. | 0.403613 | ||||||||
\(329\) | 152197. | 0.0775207 | ||||||||
\(330\) | 237.545 | + | 1025.25i | 0.000120077 | + | 0.000518255i | ||||
\(331\) | 1.70299e6 | 0.854362 | 0.427181 | − | 0.904166i | \(-0.359507\pi\) | ||||
0.427181 | + | 0.904166i | \(0.359507\pi\) | |||||||
\(332\) | 1.04434e6 | 0.519992 | ||||||||
\(333\) | 180824. | + | 369272.i | 0.0893605 | + | 0.182489i | ||||
\(334\) | 1.68425e6 | 0.826116 | ||||||||
\(335\) | 2172.55i | 0.00105769i | ||||||||
\(336\) | 140968. | + | 608422.i | 0.0681198 | + | 0.294006i | ||||
\(337\) | − | 1.30869e6i | − | 0.627716i | −0.949470 | − | 0.313858i | \(-0.898378\pi\) | ||
0.949470 | − | 0.313858i | \(-0.101622\pi\) | |||||||
\(338\) | 793684.i | 0.377882i | ||||||||
\(339\) | −3.80211e6 | + | 880930.i | −1.79691 | + | 0.416334i | ||||
\(340\) | 927.914 | 0.000435322 | ||||||||
\(341\) | −4.54133e6 | −2.11494 | ||||||||
\(342\) | −285954. | + | 140025.i | −0.132200 | + | 0.0647352i | ||||
\(343\) | − | 1.42752e6i | − | 0.655158i | ||||||
\(344\) | −1.36831e6 | −0.623429 | ||||||||
\(345\) | −375.775 | + | 1241.68i | −0.000169973 | + | 0.000561647i | ||||
\(346\) | −1.95530e6 | −0.878057 | ||||||||
\(347\) | 165579.i | 0.0738212i | 0.999319 | + | 0.0369106i | \(0.0117517\pi\) | ||||
−0.999319 | + | 0.0369106i | \(0.988248\pi\) | |||||||
\(348\) | −81315.3 | − | 350958.i | −0.0359935 | − | 0.155349i | ||||
\(349\) | −703244. | −0.309060 | −0.154530 | − | 0.987988i | \(-0.549386\pi\) | ||||
−0.154530 | + | 0.987988i | \(0.549386\pi\) | |||||||
\(350\) | 1.95626e6 | 0.853604 | ||||||||
\(351\) | −1.22164e6 | + | 994038.i | −0.529269 | + | 0.430661i | ||||
\(352\) | − | 526869.i | − | 0.226645i | ||||||
\(353\) | − | 2.81277e6i | − | 1.20143i | −0.799465 | − | 0.600713i | \(-0.794883\pi\) | ||
0.799465 | − | 0.600713i | \(-0.205117\pi\) | |||||||
\(354\) | 478995. | − | 110981.i | 0.203153 | − | 0.0470694i | ||||
\(355\) | − | 1451.75i | − | 0.000611395i | ||||||
\(356\) | 1.86435e6 | 0.779655 | ||||||||
\(357\) | −973535. | − | 4.20180e6i | −0.404279 | − | 1.74488i | ||||
\(358\) | −58415.1 | −0.0240889 | ||||||||
\(359\) | 1.53783e6 | 0.629757 | 0.314879 | − | 0.949132i | \(-0.398036\pi\) | ||||
0.314879 | + | 0.949132i | \(0.398036\pi\) | |||||||
\(360\) | 224.357 | + | 458.175i | 9.12398e−5 | + | 0.000186327i | ||||
\(361\) | 2.36880e6 | 0.956665 | ||||||||
\(362\) | −2.23364e6 | −0.895863 | ||||||||
\(363\) | −1.57451e6 | + | 364806.i | −0.627160 | + | 0.145310i | ||||
\(364\) | 1.04112e6i | 0.411856i | ||||||||
\(365\) | −1206.16 | −0.000473886 | ||||||||
\(366\) | 2.06181e6 | − | 477710.i | 0.804535 | − | 0.186407i | ||||
\(367\) | 1.90400e6i | 0.737909i | 0.929448 | + | 0.368954i | \(0.120284\pi\) | ||||
−0.929448 | + | 0.368954i | \(0.879716\pi\) | |||||||
\(368\) | 323581. | − | 563123.i | 0.124556 | − | 0.216762i | ||||
\(369\) | −1.31315e6 | − | 2.68166e6i | −0.502050 | − | 1.02527i | ||||
\(370\) | 222.019 | 8.43114e−5 | ||||||||
\(371\) | 2.54192e6i | 0.958797i | ||||||||
\(372\) | −2.14461e6 | + | 496895.i | −0.803510 | + | 0.186169i | ||||
\(373\) | − | 2.21342e6i | − | 0.823745i | −0.911242 | − | 0.411872i | \(-0.864875\pi\) | ||
0.911242 | − | 0.411872i | \(-0.135125\pi\) | |||||||
\(374\) | 3.63859e6i | 1.34510i | ||||||||
\(375\) | 3113.48 | − | 721.377i | 0.00114332 | − | 0.000264901i | ||||
\(376\) | −62240.1 | −0.0227039 | ||||||||
\(377\) | − | 600551.i | − | 0.217619i | ||||||
\(378\) | 1.83933e6 | − | 1.49664e6i | 0.662109 | − | 0.538751i | ||||
\(379\) | 3.50556e6i | 1.25360i | 0.779180 | + | 0.626800i | \(0.215636\pi\) | ||||
−0.779180 | + | 0.626800i | \(0.784364\pi\) | |||||||
\(380\) | 171.926i | 6.10776e-5i | ||||||||
\(381\) | 92120.0 | − | 21343.7i | 0.0325119 | − | 0.00753283i | ||||
\(382\) | − | 41621.5i | − | 0.0145935i | ||||||
\(383\) | 3.74107e6 | 1.30316 | 0.651581 | − | 0.758579i | \(-0.274106\pi\) | ||||
0.651581 | + | 0.758579i | \(0.274106\pi\) | |||||||
\(384\) | −57648.0 | − | 248810.i | −0.0199506 | − | 0.0861073i | ||||
\(385\) | − | 2641.42i | − | 0.000908208i | ||||||
\(386\) | 1.20295e6i | 0.410940i | ||||||||
\(387\) | 2.28479e6 | + | 4.66591e6i | 0.775477 | + | 1.58365i | ||||
\(388\) | 2.01829e6i | 0.680618i | ||||||||
\(389\) | −5.57331e6 | −1.86741 | −0.933704 | − | 0.358045i | \(-0.883444\pi\) | ||||
−0.933704 | + | 0.358045i | \(0.883444\pi\) | |||||||
\(390\) | 191.957 | + | 828.492i | 6.39062e−5 | + | 0.000275821i | ||||
\(391\) | −2.23467e6 | + | 3.88896e6i | −0.739216 | + | 1.28645i | ||||
\(392\) | − | 491874.i | − | 0.161673i | ||||||
\(393\) | −71061.8 | − | 306704.i | −0.0232089 | − | 0.100170i | ||||
\(394\) | −2.35985e6 | −0.765850 | ||||||||
\(395\) | − | 644.934i | − | 0.000207981i | ||||||
\(396\) | −1.79662e6 | + | 879763.i | −0.575729 | + | 0.281921i | ||||
\(397\) | −3.28582e6 | −1.04633 | −0.523164 | − | 0.852232i | \(-0.675249\pi\) | ||||
−0.523164 | + | 0.852232i | \(0.675249\pi\) | |||||||
\(398\) | −310979. | −0.0984064 | ||||||||
\(399\) | 778517. | − | 180378.i | 0.244814 | − | 0.0567221i | ||||
\(400\) | −800000. | −0.250000 | ||||||||
\(401\) | −746282. | −0.231762 | −0.115881 | − | 0.993263i | \(-0.536969\pi\) | ||||
−0.115881 | + | 0.993263i | \(0.536969\pi\) | |||||||
\(402\) | −4.02309e6 | + | 932130.i | −1.24164 | + | 0.287681i | ||||
\(403\) | −3.66980e6 | −1.12559 | ||||||||
\(404\) | 2.10162e6i | 0.640621i | ||||||||
\(405\) | 1187.74 | − | 1530.11i | 0.000359819 | − | 0.000463539i | ||||
\(406\) | 904200.i | 0.272238i | ||||||||
\(407\) | 870594.i | 0.260513i | ||||||||
\(408\) | 398121. | + | 1.71830e6i | 0.118403 | + | 0.511032i | ||||
\(409\) | −3.62534e6 | −1.07162 | −0.535809 | − | 0.844339i | \(-0.679993\pi\) | ||||
−0.535809 | + | 0.844339i | \(0.679993\pi\) | |||||||
\(410\) | −1612.31 | −0.000473683 | ||||||||
\(411\) | 670334. | − | 155313.i | 0.195743 | − | 0.0453527i | ||||
\(412\) | − | 981204.i | − | 0.284785i | ||||||
\(413\) | −1.23407e6 | −0.356012 | ||||||||
\(414\) | −2.46056e6 | − | 163110.i | −0.705558 | − | 0.0467715i | ||||
\(415\) | −2141.11 | −0.000610267 | ||||||||
\(416\) | − | 425757.i | − | 0.120623i | ||||||
\(417\) | −603386. | + | 139801.i | −0.169924 | + | 0.0393706i | ||||
\(418\) | −674164. | −0.188723 | ||||||||
\(419\) | 330982. | 0.0921020 | 0.0460510 | − | 0.998939i | \(-0.485336\pi\) | ||||
0.0460510 | + | 0.998939i | \(0.485336\pi\) | |||||||
\(420\) | −289.014 | − | 1247.39i | −7.99458e−5 | − | 0.000345048i | ||||
\(421\) | − | 96617.4i | − | 0.0265675i | −0.999912 | − | 0.0132837i | \(-0.995772\pi\) | ||
0.999912 | − | 0.0132837i | \(-0.00422847\pi\) | |||||||
\(422\) | − | 1.63219e6i | − | 0.446160i | ||||||
\(423\) | 103928. | + | 212238.i | 0.0282412 | + | 0.0576731i | ||||
\(424\) | − | 1.03950e6i | − | 0.280808i | ||||||
\(425\) | 5.52484e6 | 1.48371 | ||||||||
\(426\) | 2.68833e6 | − | 622873.i | 0.717727 | − | 0.166294i | ||||
\(427\) | −5.31198e6 | −1.40989 | ||||||||
\(428\) | 1.37239e6 | 0.362132 | ||||||||
\(429\) | −3.24873e6 | + | 752713.i | −0.852256 | + | 0.197463i | ||||
\(430\) | 2805.31 | 0.000731661 | ||||||||
\(431\) | 2.74215e6 | 0.711047 | 0.355523 | − | 0.934667i | \(-0.384303\pi\) | ||||
0.355523 | + | 0.934667i | \(0.384303\pi\) | |||||||
\(432\) | −752180. | + | 612041.i | −0.193916 | + | 0.157787i | ||||
\(433\) | − | 751889.i | − | 0.192723i | −0.995346 | − | 0.0963617i | \(-0.969279\pi\) | ||
0.995346 | − | 0.0963617i | \(-0.0307205\pi\) | |||||||
\(434\) | 5.52532e6 | 1.40810 | ||||||||
\(435\) | 166.713 | + | 719.537i | 4.22422e−5 | + | 0.000182318i | ||||
\(436\) | − | 2.83509e6i | − | 0.714251i | ||||||
\(437\) | −720553. | − | 414044.i | −0.180494 | − | 0.103715i | ||||
\(438\) | −517503. | − | 2.23355e6i | −0.128892 | − | 0.556302i | ||||
\(439\) | 6.44215e6 | 1.59540 | 0.797699 | − | 0.603055i | \(-0.206050\pi\) | ||||
0.797699 | + | 0.603055i | \(0.206050\pi\) | |||||||
\(440\) | 1080.19i | 0.000265992i | ||||||||
\(441\) | −1.67729e6 | + | 821328.i | −0.410687 | + | 0.201104i | ||||
\(442\) | 2.94030e6i | 0.715874i | ||||||||
\(443\) | 5.82910e6i | 1.41121i | 0.708605 | + | 0.705605i | \(0.249325\pi\) | ||||
−0.708605 | + | 0.705605i | \(0.750675\pi\) | |||||||
\(444\) | 95257.2 | + | 411132.i | 0.0229319 | + | 0.0989746i | ||||
\(445\) | −3822.30 | −0.000915008 | ||||||||
\(446\) | − | 3.89266e6i | − | 0.926637i | ||||||
\(447\) | −2.04885e6 | + | 474707.i | −0.484999 | + | 0.112372i | ||||
\(448\) | 641028.i | 0.150897i | ||||||||
\(449\) | − | 3.08357e6i | − | 0.721835i | −0.932598 | − | 0.360917i | \(-0.882464\pi\) | ||
0.932598 | − | 0.360917i | \(-0.117536\pi\) | |||||||
\(450\) | 1.33583e6 | + | 2.72799e6i | 0.310972 | + | 0.635056i | ||||
\(451\) | − | 6.32226e6i | − | 1.46363i | ||||||
\(452\) | −4.00587e6 | −0.922255 | ||||||||
\(453\) | 7.55076e6 | − | 1.74947e6i | 1.72880 | − | 0.400554i | ||||
\(454\) | − | 3.27850e6i | − | 0.746511i | ||||||
\(455\) | − | 2134.50i | − | 0.000483357i | ||||||
\(456\) | −318369. | + | 73764.5i | −0.0717000 | + | 0.0166125i | ||||
\(457\) | 1.88406e6i | 0.421993i | 0.977487 | + | 0.210997i | \(0.0676709\pi\) | ||||
−0.977487 | + | 0.210997i | \(0.932329\pi\) | |||||||
\(458\) | −2.53583e6 | −0.564879 | ||||||||
\(459\) | 5.19460e6 | − | 4.22679e6i | 1.15085 | − | 0.936438i | ||||
\(460\) | −663.409 | + | 1154.52i | −0.000146180 | + | 0.000254394i | ||||
\(461\) | 276893.i | 0.0606820i | 0.999540 | + | 0.0303410i | \(0.00965933\pi\) | ||||
−0.999540 | + | 0.0303410i | \(0.990341\pi\) | |||||||
\(462\) | 4.89134e6 | − | 1.13330e6i | 1.06616 | − | 0.247024i | ||||
\(463\) | −2.39789e6 | −0.519848 | −0.259924 | − | 0.965629i | \(-0.583698\pi\) | ||||
−0.259924 | + | 0.965629i | \(0.583698\pi\) | |||||||
\(464\) | − | 369766.i | − | 0.0797320i | ||||||
\(465\) | 4396.90 | − | 1018.74i | 0.000943005 | − | 0.000218489i | ||||
\(466\) | 5.23359e6 | 1.11644 | ||||||||
\(467\) | −1.16343e6 | −0.246860 | −0.123430 | − | 0.992353i | \(-0.539389\pi\) | ||||
−0.123430 | + | 0.992353i | \(0.539389\pi\) | |||||||
\(468\) | −1.45183e6 | + | 710927.i | −0.306409 | + | 0.150041i | ||||
\(469\) | 1.03650e7 | 2.17589 | ||||||||
\(470\) | 127.605 | 2.66455e−5 | ||||||||
\(471\) | −1.43467e6 | − | 6.19207e6i | −0.297989 | − | 1.28613i | ||||
\(472\) | 504664. | 0.104267 | ||||||||
\(473\) | 1.10003e7i | 2.26075i | ||||||||
\(474\) | 1.19428e6 | − | 276709.i | 0.244152 | − | 0.0565688i | ||||
\(475\) | 1.02365e6i | 0.208170i | ||||||||
\(476\) | − | 4.42697e6i | − | 0.895549i | ||||||
\(477\) | −3.54469e6 | + | 1.73575e6i | −0.713316 | + | 0.349294i | ||||
\(478\) | 1.61411e6 | 0.323119 | ||||||||
\(479\) | 2.38466e6 | 0.474884 | 0.237442 | − | 0.971402i | \(-0.423691\pi\) | ||||
0.237442 | + | 0.971402i | \(0.423691\pi\) | |||||||
\(480\) | 118.190 | + | 510.112i | 2.34142e−5 | + | 0.000101056i | ||||
\(481\) | 703518.i | 0.138648i | ||||||||
\(482\) | −254077. | −0.0498136 | ||||||||
\(483\) | 5.92394e6 | + | 1.79278e6i | 1.15543 | + | 0.349670i | ||||
\(484\) | −1.65889e6 | −0.321887 | ||||||||
\(485\) | − | 4137.91i | − | 0.000798778i | ||||||
\(486\) | 3.34304e6 | + | 1.54295e6i | 0.642024 | + | 0.296320i | ||||
\(487\) | −1.13750e6 | −0.217335 | −0.108668 | − | 0.994078i | \(-0.534658\pi\) | ||||
−0.108668 | + | 0.994078i | \(0.534658\pi\) | |||||||
\(488\) | 2.17230e6 | 0.412924 | ||||||||
\(489\) | 2.56153e6 | − | 593494.i | 0.484426 | − | 0.112239i | ||||
\(490\) | 1008.44i | 0.000189741i | ||||||||
\(491\) | 1.41268e6i | 0.264448i | 0.991220 | + | 0.132224i | \(0.0422118\pi\) | ||||
−0.991220 | + | 0.132224i | \(0.957788\pi\) | |||||||
\(492\) | −691759. | − | 2.98564e6i | −0.128837 | − | 0.556065i | ||||
\(493\) | 2.55363e6i | 0.473195i | ||||||||
\(494\) | −544785. | −0.100440 | ||||||||
\(495\) | 3683.44 | − | 1803.70i | 0.000675680 | − | 0.000330865i | ||||
\(496\) | −2.25954e6 | −0.412398 | ||||||||
\(497\) | −6.92615e6 | −1.25777 | ||||||||
\(498\) | −918643. | − | 3.96488e6i | −0.165987 | − | 0.716403i | ||||
\(499\) | 6.71999e6 | 1.20814 | 0.604070 | − | 0.796931i | \(-0.293545\pi\) | ||||
0.604070 | + | 0.796931i | \(0.293545\pi\) | |||||||
\(500\) | 3280.33 | 0.000586803 | ||||||||
\(501\) | −1.48153e6 | − | 6.39434e6i | −0.263704 | − | 1.13815i | ||||
\(502\) | − | 1.00957e6i | − | 0.178804i | ||||||
\(503\) | −7.30586e6 | −1.28751 | −0.643756 | − | 0.765231i | \(-0.722625\pi\) | ||||
−0.643756 | + | 0.765231i | \(0.722625\pi\) | |||||||
\(504\) | 2.18590e6 | − | 1.07038e6i | 0.383313 | − | 0.187700i | ||||
\(505\) | − | 4308.76i | − | 0.000751837i | ||||||
\(506\) | −4.52716e6 | − | 2.60139e6i | −0.786049 | − | 0.451679i | ||||
\(507\) | 3.01326e6 | − | 698156.i | 0.520614 | − | 0.120624i | ||||
\(508\) | 97056.8 | 0.0166866 | ||||||||
\(509\) | − | 3.42230e6i | − | 0.585496i | −0.956190 | − | 0.292748i | \(-0.905430\pi\) | ||
0.956190 | − | 0.292748i | \(-0.0945697\pi\) | |||||||
\(510\) | −816.230 | − | 3522.86i | −0.000138959 | − | 0.000599750i | ||||
\(511\) | 5.75446e6i | 0.974883i | ||||||||
\(512\) | − | 262144.i | − | 0.0441942i | ||||||
\(513\) | 783148. | + | 962465.i | 0.131386 | + | 0.161470i | ||||
\(514\) | 2.83229e6 | 0.472858 | ||||||||
\(515\) | 2011.67i | 0.000334225i | ||||||||
\(516\) | 1.20362e6 | + | 5.19483e6i | 0.199005 | + | 0.858909i | ||||
\(517\) | 500373.i | 0.0823317i | ||||||||
\(518\) | − | 1.05923e6i | − | 0.173446i | ||||||
\(519\) | 1.71996e6 | + | 7.42337e6i | 0.280285 | + | 1.20971i | ||||
\(520\) | 872.891i | 0.000141564i | ||||||||
\(521\) | 8.26650e6 | 1.33422 | 0.667110 | − | 0.744960i | \(-0.267531\pi\) | ||||
0.667110 | + | 0.744960i | \(0.267531\pi\) | |||||||
\(522\) | −1.26090e6 | + | 617434.i | −0.202537 | + | 0.0991777i | ||||
\(523\) | − | 5.11333e6i | − | 0.817427i | −0.912663 | − | 0.408714i | \(-0.865977\pi\) | ||
0.912663 | − | 0.408714i | \(-0.134023\pi\) | |||||||
\(524\) | − | 323140.i | − | 0.0514118i | ||||||
\(525\) | −1.72080e6 | − | 7.42703e6i | −0.272479 | − | 1.17603i | ||||
\(526\) | − | 3.23685e6i | − | 0.510104i | ||||||
\(527\) | 1.56045e7 | 2.44751 | ||||||||
\(528\) | −2.00028e6 | + | 463455.i | −0.312253 | + | 0.0723473i | ||||
\(529\) | −3.24100e6 | − | 5.56079e6i | −0.503548 | − | 0.863968i | ||||
\(530\) | 2131.19i | 0.000329558i | ||||||||
\(531\) | −842686. | − | 1.72090e6i | −0.129697 | − | 0.264862i | ||||
\(532\) | 820238. | 0.125649 | ||||||||
\(533\) | − | 5.10895e6i | − | 0.778958i | ||||||
\(534\) | −1.63996e6 | − | 7.07808e6i | −0.248874 | − | 1.07414i | ||||
\(535\) | −2813.68 | −0.000425001 | ||||||||
\(536\) | −4.23869e6 | −0.637265 | ||||||||
\(537\) | 51384.3 | + | 221776.i | 0.00768943 | + | 0.0331878i | ||||
\(538\) | −6.33226e6 | −0.943198 | ||||||||
\(539\) | −3.95436e6 | −0.586280 | ||||||||
\(540\) | 1542.13 | − | 1254.81i | 0.000227581 | − | 0.000185180i | ||||
\(541\) | 1.38456e6 | 0.203385 | 0.101693 | − | 0.994816i | \(-0.467574\pi\) | ||||
0.101693 | + | 0.994816i | \(0.467574\pi\) | |||||||
\(542\) | − | 2.90164e6i | − | 0.424274i | ||||||
\(543\) | 1.96480e6 | + | 8.48011e6i | 0.285968 | + | 1.23425i | ||||
\(544\) | 1.81038e6i | 0.262285i | ||||||||
\(545\) | 5812.53i | 0.000838250i | ||||||||
\(546\) | 3.95264e6 | − | 915806.i | 0.567421 | − | 0.131469i | ||||
\(547\) | −7.02754e6 | −1.00423 | −0.502117 | − | 0.864800i | \(-0.667445\pi\) | ||||
−0.502117 | + | 0.864800i | \(0.667445\pi\) | |||||||
\(548\) | 706257. | 0.100464 | ||||||||
\(549\) | −3.62729e6 | − | 7.40752e6i | −0.513631 | − | 1.04892i | ||||
\(550\) | 6.43151e6i | 0.906580i | ||||||||
\(551\) | −473141. | −0.0663913 | ||||||||
\(552\) | −2.42255e6 | − | 733145.i | −0.338397 | − | 0.102410i | ||||
\(553\) | −3.07691e6 | −0.427860 | ||||||||
\(554\) | 3.83855e6i | 0.531365i | ||||||||
\(555\) | −195.297 | − | 842.906i | −2.69131e−5 | − | 0.000116157i | ||||
\(556\) | −635722. | −0.0872128 | ||||||||
\(557\) | −773371. | −0.105621 | −0.0528104 | − | 0.998605i | \(-0.516818\pi\) | ||||
−0.0528104 | + | 0.998605i | \(0.516818\pi\) | |||||||
\(558\) | 3.77297e6 | + | 7.70502e6i | 0.512977 | + | 1.04758i | ||||
\(559\) | 8.88926e6i | 1.20320i | ||||||||
\(560\) | − | 1314.24i | − | 0.000177094i | ||||||
\(561\) | 1.38141e7 | − | 3.20065e6i | 1.85316 | − | 0.429369i | ||||
\(562\) | 4.94309e6i | 0.660174i | ||||||||
\(563\) | −5.10022e6 | −0.678138 | −0.339069 | − | 0.940762i | \(-0.610112\pi\) | ||||
−0.339069 | + | 0.940762i | \(0.610112\pi\) | |||||||
\(564\) | 54748.9 | + | 236297.i | 0.00724732 | + | 0.0312796i | ||||
\(565\) | 8212.86 | 0.00108236 | ||||||||
\(566\) | −8.57423e6 | −1.12500 | ||||||||
\(567\) | −7.30000e6 | − | 5.66658e6i | −0.953598 | − | 0.740224i | ||||
\(568\) | 2.83240e6 | 0.368370 | ||||||||
\(569\) | 1.38405e7 | 1.79214 | 0.896068 | − | 0.443917i | \(-0.146411\pi\) | ||||
0.896068 | + | 0.443917i | \(0.146411\pi\) | |||||||
\(570\) | 652.723 | − | 151.233i | 8.41476e−5 | − | 1.94966e-5i | ||||
\(571\) | − | 2.31043e6i | − | 0.296553i | −0.988946 | − | 0.148277i | \(-0.952627\pi\) | ||
0.988946 | − | 0.148277i | \(-0.0473726\pi\) | |||||||
\(572\) | −3.42283e6 | −0.437416 | ||||||||
\(573\) | −158018. | + | 36611.9i | −0.0201057 | + | 0.00465839i | ||||
\(574\) | 7.69213e6i | 0.974467i | ||||||||
\(575\) | −3.94997e6 | + | 6.87406e6i | −0.498223 | + | 0.867049i | ||||
\(576\) | −893909. | + | 437727.i | −0.112263 | + | 0.0549726i | ||||
\(577\) | −6.82028e6 | −0.852830 | −0.426415 | − | 0.904528i | \(-0.640224\pi\) | ||||
−0.426415 | + | 0.904528i | \(0.640224\pi\) | |||||||
\(578\) | − | 6.82317e6i | − | 0.849506i | ||||||
\(579\) | 4.56704e6 | − | 1.05816e6i | 0.566159 | − | 0.131176i | ||||
\(580\) | 758.098i | 9.35740e-5i | ||||||||
\(581\) | 1.02150e7i | 1.25545i | ||||||||
\(582\) | 7.66251e6 | − | 1.77536e6i | 0.937700 | − | 0.217260i | ||||
\(583\) | −8.35694e6 | −1.01830 | ||||||||
\(584\) | − | 2.35325e6i | − | 0.285520i | ||||||
\(585\) | 2976.55 | − | 1457.55i | 0.000359603 | − | 0.000176089i | ||||
\(586\) | − | 9.84622e6i | − | 1.18447i | ||||||
\(587\) | − | 1.28259e7i | − | 1.53636i | −0.640233 | − | 0.768181i | \(-0.721162\pi\) | ||
0.640233 | − | 0.768181i | \(-0.278838\pi\) | |||||||
\(588\) | −1.86742e6 | + | 432672.i | −0.222740 | + | 0.0516078i | ||||
\(589\) | 2.89123e6i | 0.343396i | ||||||||
\(590\) | −1034.67 | −0.000122369 | ||||||||
\(591\) | 2.07582e6 | + | 8.95927e6i | 0.244467 | + | 1.05512i | ||||
\(592\) | 433165.i | 0.0507983i | ||||||||
\(593\) | − | 1.54759e6i | − | 0.180726i | −0.995909 | − | 0.0903628i | \(-0.971197\pi\) | ||
0.995909 | − | 0.0903628i | \(-0.0288027\pi\) | |||||||
\(594\) | 4.92044e6 | + | 6.04707e6i | 0.572186 | + | 0.703200i | ||||
\(595\) | 9076.21i | 0.00105102i | ||||||||
\(596\) | −2.15864e6 | −0.248923 | ||||||||
\(597\) | 273549. | + | 1.18065e6i | 0.0314123 | + | 0.135576i | ||||
\(598\) | −3.65835e6 | − | 2.10216e6i | −0.418343 | − | 0.240388i | ||||
\(599\) | 1.11713e7i | 1.27215i | 0.771627 | + | 0.636075i | \(0.219443\pi\) | ||||
−0.771627 | + | 0.636075i | \(0.780557\pi\) | |||||||
\(600\) | 703711. | + | 3.03723e6i | 0.0798025 | + | 0.344429i | ||||
\(601\) | −1.19470e7 | −1.34918 | −0.674592 | − | 0.738191i | \(-0.735680\pi\) | ||||
−0.674592 | + | 0.738191i | \(0.735680\pi\) | |||||||
\(602\) | − | 1.33838e7i | − | 1.50518i | ||||||
\(603\) | 7.07774e6 | + | 1.44539e7i | 0.792686 | + | 1.61880i | ||||
\(604\) | 7.95540e6 | 0.887299 | ||||||||
\(605\) | 3401.06 | 0.000377769 | ||||||||
\(606\) | 7.97889e6 | − | 1.84867e6i | 0.882594 | − | 0.204493i | ||||
\(607\) | 181705. | 0.0200168 | 0.0100084 | − | 0.999950i | \(-0.496814\pi\) | ||||
0.0100084 | + | 0.999950i | \(0.496814\pi\) | |||||||
\(608\) | −335431. | −0.0367997 | ||||||||
\(609\) | 3.43283e6 | − | 795370.i | 0.375067 | − | 0.0869012i | ||||
\(610\) | −4453.66 | −0.000484610 | ||||||||
\(611\) | 404346.i | 0.0438177i | ||||||||
\(612\) | 6.17339e6 | − | 3.02296e6i | 0.666262 | − | 0.326253i | ||||
\(613\) | 2.64180e6i | 0.283954i | 0.989870 | + | 0.141977i | \(0.0453460\pi\) | ||||
−0.989870 | + | 0.141977i | \(0.954654\pi\) | |||||||
\(614\) | − | 2.40177e6i | − | 0.257105i | ||||||
\(615\) | 1418.25 | + | 6121.19i | 0.000151204 | + | 0.000652601i | ||||
\(616\) | 5.15347e6 | 0.547202 | ||||||||
\(617\) | 4.66150e6 | 0.492961 | 0.246481 | − | 0.969148i | \(-0.420726\pi\) | ||||
0.246481 | + | 0.969148i | \(0.420726\pi\) | |||||||
\(618\) | −3.72518e6 | + | 863106.i | −0.392353 | + | 0.0909061i | ||||
\(619\) | 1.13068e6i | 0.118608i | 0.998240 | + | 0.0593038i | \(0.0188881\pi\) | ||||
−0.998240 | + | 0.0593038i | \(0.981112\pi\) | |||||||
\(620\) | 4632.53 | 0.000483993 | ||||||||
\(621\) | 1.54515e6 | + | 9.48509e6i | 0.160783 | + | 0.986990i | ||||
\(622\) | −1.23676e7 | −1.28176 | ||||||||
\(623\) | 1.82358e7i | 1.88237i | ||||||||
\(624\) | −1.61641e6 | + | 374513.i | −0.166184 | + | 0.0385040i | ||||
\(625\) | 9.76561e6 | 0.999999 | ||||||||
\(626\) | 3.36918e6 | 0.343628 | ||||||||
\(627\) | 593022. | + | 2.55949e6i | 0.0602423 | + | 0.260007i | ||||
\(628\) | − | 6.52390e6i | − | 0.660098i | ||||||
\(629\) | − | 2.99146e6i | − | 0.301479i | ||||||
\(630\) | −4481.55 | + | 2194.51i | −0.000449859 | + | 0.000220286i | ||||
\(631\) | − | 1.30238e7i | − | 1.30216i | −0.759010 | − | 0.651079i | \(-0.774317\pi\) | ||
0.759010 | − | 0.651079i | \(-0.225683\pi\) | |||||||
\(632\) | 1.25828e6 | 0.125310 | ||||||||
\(633\) | −6.19669e6 | + | 1.43574e6i | −0.614682 | + | 0.142419i | ||||
\(634\) | −1.22819e7 | −1.21351 | ||||||||
\(635\) | −198.986 | −1.95835e−5 | ||||||||
\(636\) | −3.94651e6 | + | 914385.i | −0.386874 | + | 0.0896368i | ||||
\(637\) | −3.19548e6 | −0.312024 | ||||||||
\(638\) | −2.97269e6 | −0.289134 | ||||||||
\(639\) | −4.72953e6 | − | 9.65847e6i | −0.458211 | − | 0.935742i | ||||
\(640\) | 537.449i | 5.18666e-5i | ||||||||
\(641\) | 7.86815e6 | 0.756358 | 0.378179 | − | 0.925733i | \(-0.376550\pi\) | ||||
0.378179 | + | 0.925733i | \(0.376550\pi\) | |||||||
\(642\) | −1.20721e6 | − | 5.21033e6i | −0.115596 | − | 0.498916i | ||||
\(643\) | 1.56004e7i | 1.48802i | 0.668169 | + | 0.744009i | \(0.267078\pi\) | ||||
−0.668169 | + | 0.744009i | \(0.732922\pi\) | |||||||
\(644\) | 5.50808e6 | + | 3.16505e6i | 0.523342 | + | 0.300722i | ||||
\(645\) | −2467.66 | − | 10650.5i | −0.000233554 | − | 0.00100802i | ||||
\(646\) | 2.31650e6 | 0.218400 | ||||||||
\(647\) | − | 1.61792e6i | − | 0.151949i | −0.997110 | − | 0.0759744i | \(-0.975793\pi\) | ||
0.997110 | − | 0.0759744i | \(-0.0242067\pi\) | |||||||
\(648\) | 2.98529e6 | + | 2.31731e6i | 0.279286 | + | 0.216794i | ||||
\(649\) | − | 4.05719e6i | − | 0.378106i | ||||||
\(650\) | 5.19723e6i | 0.482490i | ||||||||
\(651\) | −4.86029e6 | − | 2.09771e7i | −0.449479 | − | 1.93996i | ||||
\(652\) | 2.69881e6 | 0.248630 | ||||||||
\(653\) | 1.13742e7i | 1.04385i | 0.852992 | + | 0.521925i | \(0.174786\pi\) | ||||
−0.852992 | + | 0.521925i | \(0.825214\pi\) | |||||||
\(654\) | −1.07636e7 | + | 2.49386e6i | −0.984037 | + | 0.227996i | ||||
\(655\) | 662.505i | 6.03373e-5i | ||||||||
\(656\) | − | 3.14565e6i | − | 0.285398i | ||||||
\(657\) | −8.02456e6 | + | 3.92944e6i | −0.725284 | + | 0.355155i | ||||
\(658\) | − | 608790.i | − | 0.0548154i | ||||||
\(659\) | −1.82620e7 | −1.63808 | −0.819040 | − | 0.573736i | \(-0.805494\pi\) | ||||
−0.819040 | + | 0.573736i | \(0.805494\pi\) | |||||||
\(660\) | 4100.99 | − | 950.178i | 0.000366462 | − | 8.49073e-5i | ||||
\(661\) | 1.36419e7i | 1.21443i | 0.794538 | + | 0.607215i | \(0.207713\pi\) | ||||
−0.794538 | + | 0.607215i | \(0.792287\pi\) | |||||||
\(662\) | − | 6.81196e6i | − | 0.604125i | ||||||
\(663\) | 1.11630e7 | − | 2.58641e6i | 0.986272 | − | 0.228514i | ||||
\(664\) | − | 4.17736e6i | − | 0.367690i | ||||||
\(665\) | −1681.66 | −0.000147463 | ||||||||
\(666\) | 1.47709e6 | − | 723296.i | 0.129039 | − | 0.0631874i | ||||
\(667\) | −3.17724e6 | − | 1.82571e6i | −0.276526 | − | 0.158897i | ||||
\(668\) | − | 6.73701e6i | − | 0.584152i | ||||||
\(669\) | −1.47787e7 | + | 3.42414e6i | −1.27664 | + | 0.295792i | ||||
\(670\) | 8690.19 | 0.000747898 | ||||||||
\(671\) | − | 1.74639e7i | − | 1.49739i | ||||||
\(672\) | 2.43369e6 | − | 563873.i | 0.207894 | − | 0.0481680i | ||||
\(673\) | −5.50902e6 | −0.468853 | −0.234426 | − | 0.972134i | \(-0.575321\pi\) | ||||
−0.234426 | + | 0.972134i | \(0.575321\pi\) | |||||||
\(674\) | −5.23477e6 | −0.443862 | ||||||||
\(675\) | 9.18189e6 | − | 7.47120e6i | 0.775662 | − | 0.631148i | ||||
\(676\) | 3.17474e6 | 0.267203 | ||||||||
\(677\) | 1.22229e7 | 1.02495 | 0.512476 | − | 0.858702i | \(-0.328729\pi\) | ||||
0.512476 | + | 0.858702i | \(0.328729\pi\) | |||||||
\(678\) | 3.52372e6 | + | 1.52085e7i | 0.294393 | + | 1.27061i | ||||
\(679\) | −1.97415e7 | −1.64326 | ||||||||
\(680\) | − | 3711.66i | − | 0.000307819i | ||||||
\(681\) | −1.24470e7 | + | 2.88390e6i | −1.02848 | + | 0.238294i | ||||
\(682\) | 1.81653e7i | 1.49549i | ||||||||
\(683\) | − | 2.02081e7i | − | 1.65758i | −0.559561 | − | 0.828789i | \(-0.689030\pi\) | ||
0.559561 | − | 0.828789i | \(-0.310970\pi\) | |||||||
\(684\) | 560100. | + | 1.14382e6i | 0.0457747 | + | 0.0934794i | ||||
\(685\) | −1447.97 | −0.000117906 | ||||||||
\(686\) | −5.71007e6 | −0.463267 | ||||||||
\(687\) | 2.23061e6 | + | 9.62737e6i | 0.180315 | + | 0.778244i | ||||
\(688\) | 5.47323e6i | 0.440831i | ||||||||
\(689\) | −6.75315e6 | −0.541949 | ||||||||
\(690\) | 4966.74 | + | 1503.10i | 0.000397144 | + | 0.000120189i | ||||
\(691\) | 1.15788e7 | 0.922507 | 0.461253 | − | 0.887269i | \(-0.347400\pi\) | ||||
0.461253 | + | 0.887269i | \(0.347400\pi\) | |||||||
\(692\) | 7.82119e6i | 0.620880i | ||||||||
\(693\) | −8.60523e6 | − | 1.75733e7i | −0.680659 | − | 1.39002i | ||||
\(694\) | 662315. | 0.0521995 | ||||||||
\(695\) | 1303.36 | 0.000102354 | ||||||||
\(696\) | −1.40383e6 | + | 325261.i | −0.109848 | + | 0.0254512i | ||||
\(697\) | 2.17240e7i | 1.69378i | ||||||||
\(698\) | 2.81298e6i | 0.218538i | ||||||||
\(699\) | −4.60367e6 | − | 1.98696e7i | −0.356379 | − | 1.53814i | ||||
\(700\) | − | 7.82504e6i | − | 0.603589i | ||||||
\(701\) | 1.22850e7 | 0.944234 | 0.472117 | − | 0.881536i | \(-0.343490\pi\) | ||||
0.472117 | + | 0.881536i | \(0.343490\pi\) | |||||||
\(702\) | 3.97615e6 | + | 4.88657e6i | 0.304523 | + | 0.374250i | ||||
\(703\) | 554263. | 0.0422988 | ||||||||
\(704\) | −2.10748e6 | −0.160262 | ||||||||
\(705\) | −112.247 | − | 484.458i | −8.50551e−6 | − | 3.67099e-5i | ||||
\(706\) | −1.12511e7 | −0.849536 | ||||||||
\(707\) | −2.05566e7 | −1.54669 | ||||||||
\(708\) | −443923. | − | 1.91598e6i | −0.0332831 | − | 0.143651i | ||||
\(709\) | 2.44045e6i | 0.182328i | 0.995836 | + | 0.0911642i | \(0.0290588\pi\) | ||||
−0.995836 | + | 0.0911642i | \(0.970941\pi\) | |||||||
\(710\) | −5807.01 | −0.000432321 | ||||||||
\(711\) | −2.10107e6 | − | 4.29073e6i | −0.155872 | − | 0.318315i | ||||
\(712\) | − | 7.45740e6i | − | 0.551299i | ||||||
\(713\) | −1.11564e7 | + | 1.94153e7i | −0.821864 | + | 1.43028i | ||||
\(714\) | −1.68072e7 | + | 3.89414e6i | −1.23381 | + | 0.285868i | ||||
\(715\) | 7017.50 | 0.000513355 | ||||||||
\(716\) | 233661.i | 0.0170335i | ||||||||
\(717\) | −1.41983e6 | − | 6.12802e6i | −0.103143 | − | 0.445166i | ||||
\(718\) | − | 6.15133e6i | − | 0.445306i | ||||||
\(719\) | − | 8.55273e6i | − | 0.616996i | −0.951225 | − | 0.308498i | \(-0.900174\pi\) | ||
0.951225 | − | 0.308498i | \(-0.0998264\pi\) | |||||||
\(720\) | 1832.70 | − | 897.430i | 0.000131753 | − | 6.45163e-5i | ||||
\(721\) | 9.59746e6 | 0.687572 | ||||||||
\(722\) | − | 9.47519e6i | − | 0.676464i | ||||||
\(723\) | 223496. | + | 964614.i | 0.0159010 | + | 0.0686290i | ||||
\(724\) | 8.93456e6i | 0.633471i | ||||||||
\(725\) | 4.51375e6i | 0.318928i | ||||||||
\(726\) | 1.45922e6 | + | 6.29804e6i | 0.102750 | + | 0.443469i | ||||
\(727\) | − | 6.59873e6i | − | 0.463046i | −0.972829 | − | 0.231523i | \(-0.925629\pi\) | ||
0.972829 | − | 0.231523i | \(-0.0743708\pi\) | |||||||
\(728\) | 4.16446e6 | 0.291226 | ||||||||
\(729\) | 2.91719e6 | − | 1.40492e7i | 0.203304 | − | 0.979116i | ||||
\(730\) | 4824.65i | 0.000335088i | ||||||||
\(731\) | − | 3.77984e7i | − | 2.61625i | ||||||
\(732\) | −1.91084e6 | − | 8.24722e6i | −0.131809 | − | 0.568892i | ||||
\(733\) | 4.60639e6i | 0.316665i | 0.987386 | + | 0.158333i | \(0.0506119\pi\) | ||||
−0.987386 | + | 0.158333i | \(0.949388\pi\) | |||||||
\(734\) | 7.61602e6 | 0.521780 | ||||||||
\(735\) | 3828.60 | − | 887.067i | 0.000261410 | − | 6.05672e-5i | ||||
\(736\) | −2.25249e6 | − | 1.29433e6i | −0.153274 | − | 0.0880742i | ||||
\(737\) | 3.40765e7i | 2.31093i | ||||||||
\(738\) | −1.07266e7 | + | 5.25258e6i | −0.724974 | + | 0.355003i | ||||
\(739\) | −832395. | −0.0560684 | −0.0280342 | − | 0.999607i | \(-0.508925\pi\) | ||||
−0.0280342 | + | 0.999607i | \(0.508925\pi\) | |||||||
\(740\) | − | 888.077i | − | 5.96172e-5i | ||||||
\(741\) | 479214. | + | 2.06830e6i | 0.0320615 | + | 0.138378i | ||||
\(742\) | 1.01677e7 | 0.677972 | ||||||||
\(743\) | 1.12065e7 | 0.744728 | 0.372364 | − | 0.928087i | \(-0.378547\pi\) | ||||
0.372364 | + | 0.928087i | \(0.378547\pi\) | |||||||
\(744\) | 1.98758e6 | + | 8.57845e6i | 0.131641 | + | 0.568167i | ||||
\(745\) | 4425.67 | 0.000292138 | ||||||||
\(746\) | −8.85370e6 | −0.582476 | ||||||||
\(747\) | −1.42448e7 | + | 6.97534e6i | −0.934015 | + | 0.457366i | ||||
\(748\) | 1.45544e7 | 0.951128 | ||||||||
\(749\) | 1.34237e7i | 0.874317i | ||||||||
\(750\) | −2885.51 | − | 12453.9i | −0.000187314 | − | 0.000808449i | ||||
\(751\) | − | 1.68641e7i | − | 1.09109i | −0.838080 | − | 0.545547i | \(-0.816322\pi\) | ||
0.838080 | − | 0.545547i | \(-0.183678\pi\) | |||||||
\(752\) | 248961.i | 0.0160541i | ||||||||
\(753\) | −3.83288e6 | + | 888058.i | −0.246341 | + | 0.0570761i | ||||
\(754\) | −2.40220e6 | −0.153880 | ||||||||
\(755\) | −16310.2 | −0.00104134 | ||||||||
\(756\) | −5.98656e6 | − | 7.35731e6i | −0.380954 | − | 0.468182i | ||||
\(757\) | − | 1.67223e7i | − | 1.06061i | −0.847807 | − | 0.530305i | \(-0.822077\pi\) | ||
0.847807 | − | 0.530305i | \(-0.177923\pi\) | |||||||
\(758\) | 1.40222e7 | 0.886429 | ||||||||
\(759\) | −5.89404e6 | + | 1.94758e7i | −0.371371 | + | 1.22713i | ||||
\(760\) | 687.702 | 4.31883e−5 | ||||||||
\(761\) | 2.59693e7i | 1.62554i | 0.582582 | + | 0.812772i | \(0.302042\pi\) | ||||
−0.582582 | + | 0.812772i | \(0.697958\pi\) | |||||||
\(762\) | −85375.0 | − | 368480.i | −0.00532651 | − | 0.0229893i | ||||
\(763\) | 2.77309e7 | 1.72446 | ||||||||
\(764\) | −166486. | −0.0103192 | ||||||||
\(765\) | −12656.7 | + | 6197.70i | −0.000781929 | + | 0.000382893i | ||||
\(766\) | − | 1.49643e7i | − | 0.921475i | ||||||
\(767\) | − | 3.27857e6i | − | 0.201232i | ||||||
\(768\) | −995241. | + | 230592.i | −0.0608871 | + | 0.0141072i | ||||
\(769\) | − | 1.01967e7i | − | 0.621793i | −0.950444 | − | 0.310896i | \(-0.899371\pi\) | ||
0.950444 | − | 0.310896i | \(-0.100629\pi\) | |||||||
\(770\) | −10565.7 | −0.000642200 | ||||||||
\(771\) | −2.49140e6 | − | 1.07529e7i | −0.150941 | − | 0.651464i | ||||
\(772\) | 4.81179e6 | 0.290578 | ||||||||
\(773\) | 2.07427e7 | 1.24858 | 0.624289 | − | 0.781194i | \(-0.285389\pi\) | ||||
0.624289 | + | 0.781194i | \(0.285389\pi\) | |||||||
\(774\) | 1.86637e7 | − | 9.13916e6i | 1.11981 | − | 0.548345i | ||||
\(775\) | 2.75823e7 | 1.64959 | ||||||||
\(776\) | 8.07315e6 | 0.481270 | ||||||||
\(777\) | −4.02141e6 | + | 931740.i | −0.238960 | + | 0.0553659i | ||||
\(778\) | 2.22933e7i | 1.32046i | ||||||||
\(779\) | −4.02506e6 | −0.237645 | ||||||||
\(780\) | 3313.97 | − | 767.829i | 0.000195035 | − | 4.51885e-5i | ||||
\(781\) | − | 2.27708e7i | − | 1.33583i | ||||||
\(782\) | 1.55558e7 | + | 8.93868e6i | 0.909654 | + | 0.522705i | ||||
\(783\) | 3.45325e6 | + | 4.24394e6i | 0.201291 | + | 0.247380i | ||||
\(784\) | −1.96750e6 | −0.114320 | ||||||||
\(785\) | 13375.4i | 0.000774696i | ||||||||
\(786\) | −1.22682e6 | + | 284247.i | −0.0708310 | + | 0.0164112i | ||||
\(787\) | − | 1.91540e7i | − | 1.10236i | −0.834386 | − | 0.551180i | \(-0.814178\pi\) | ||
0.834386 | − | 0.551180i | \(-0.185822\pi\) | |||||||
\(788\) | 9.43940e6i | 0.541538i | ||||||||
\(789\) | −1.22889e7 | + | 2.84726e6i | −0.702779 | + | 0.162830i | ||||
\(790\) | −2579.74 | −0.000147064 | ||||||||
\(791\) | − | 3.91826e7i | − | 2.22665i | ||||||
\(792\) | 3.51905e6 | + | 7.18648e6i | 0.199348 | + | 0.407102i | ||||
\(793\) | − | 1.41124e7i | − | 0.796927i | ||||||
\(794\) | 1.31433e7i | 0.739866i | ||||||||
\(795\) | 8091.15 | − | 1874.68i | 0.000454038 | − | 0.000105198i | ||||
\(796\) | 1.24392e6i | 0.0695838i | ||||||||
\(797\) | 7.92762e6 | 0.442076 | 0.221038 | − | 0.975265i | \(-0.429055\pi\) | ||||
0.221038 | + | 0.975265i | \(0.429055\pi\) | |||||||
\(798\) | −721514. | − | 3.11407e6i | −0.0401086 | − | 0.173109i | ||||
\(799\) | − | 1.71934e6i | − | 0.0952783i | ||||||
\(800\) | 3.20000e6i | 0.176777i | ||||||||
\(801\) | −2.54297e7 | + | 1.24523e7i | −1.40042 | + | 0.685755i | ||||
\(802\) | 2.98513e6i | 0.163880i | ||||||||
\(803\) | −1.89187e7 | −1.03539 | ||||||||
\(804\) | 3.72852e6 | + | 1.60924e7i | 0.203421 | + | 0.877971i | ||||
\(805\) | −11292.7 | − | 6489.00i | −0.000614197 | − | 0.000352930i | ||||
\(806\) | 1.46792e7i | 0.795912i | ||||||||
\(807\) | 5.57010e6 | + | 2.40407e7i | 0.301078 | + | 1.29946i | ||||
\(808\) | 8.40648e6 | 0.452987 | ||||||||
\(809\) | − | 3.14727e7i | − | 1.69068i | −0.534226 | − | 0.845342i | \(-0.679397\pi\) | ||
0.534226 | − | 0.845342i | \(-0.320603\pi\) | |||||||
\(810\) | −6120.46 | − | 4750.96i | −0.000327772 | − | 0.000254430i | ||||
\(811\) | 2.15848e7 | 1.15238 | 0.576191 | − | 0.817315i | \(-0.304539\pi\) | ||||
0.576191 | + | 0.817315i | \(0.304539\pi\) | |||||||
\(812\) | 3.61680e6 | 0.192502 | ||||||||
\(813\) | −1.10162e7 | + | 2.55240e6i | −0.584529 | + | 0.135432i | ||||
\(814\) | 3.48238e6 | 0.184211 | ||||||||
\(815\) | −5533.11 | −0.000291793 | ||||||||
\(816\) | 6.87319e6 | − | 1.59248e6i | 0.361354 | − | 0.0837239i | ||||
\(817\) | 7.00336e6 | 0.367072 | ||||||||
\(818\) | 1.45013e7i | 0.757748i | ||||||||
\(819\) | −6.95380e6 | − | 1.42008e7i | −0.362253 | − | 0.739780i | ||||
\(820\) | 6449.22i | 0.000334945i | ||||||||
\(821\) | 3.19922e7i | 1.65648i | 0.560373 | + | 0.828240i | \(0.310658\pi\) | ||||
−0.560373 | + | 0.828240i | \(0.689342\pi\) | |||||||
\(822\) | −621252. | − | 2.68134e6i | −0.0320692 | − | 0.138411i | ||||
\(823\) | 2.18883e7 | 1.12645 | 0.563225 | − | 0.826304i | \(-0.309561\pi\) | ||||
0.563225 | + | 0.826304i | \(0.309561\pi\) | |||||||
\(824\) | −3.92482e6 | −0.201373 | ||||||||
\(825\) | 2.44175e7 | − | 5.65741e6i | 1.24901 | − | 0.289389i | ||||
\(826\) | 4.93628e6i | 0.251738i | ||||||||
\(827\) | −91163.8 | −0.00463510 | −0.00231755 | − | 0.999997i | \(-0.500738\pi\) | ||||
−0.00231755 | + | 0.999997i | \(0.500738\pi\) | |||||||
\(828\) | −652442. | + | 9.84223e6i | −0.0330724 | + | 0.498905i | ||||
\(829\) | 2.22385e7 | 1.12388 | 0.561939 | − | 0.827179i | \(-0.310056\pi\) | ||||
0.561939 | + | 0.827179i | \(0.310056\pi\) | |||||||
\(830\) | 8564.46i | 0.000431524i | ||||||||
\(831\) | 1.45732e7 | − | 3.37654e6i | 0.732070 | − | 0.169617i | ||||
\(832\) | −1.70303e6 | −0.0852931 | ||||||||
\(833\) | 1.35876e7 | 0.678471 | ||||||||
\(834\) | 559206. | + | 2.41354e6i | 0.0278392 | + | 0.120155i | ||||
\(835\) | 13812.3i | 0.000685565i | ||||||||
\(836\) | 2.69666e6i | 0.133447i | ||||||||
\(837\) | 2.59336e7 | − | 2.11019e7i | 1.27953 | − | 1.04114i | ||||
\(838\) | − | 1.32393e6i | − | 0.0651259i | ||||||
\(839\) | −2.09955e7 | −1.02972 | −0.514862 | − | 0.857273i | \(-0.672157\pi\) | ||||
−0.514862 | + | 0.857273i | \(0.672157\pi\) | |||||||
\(840\) | −4989.57 | + | 1156.06i | −0.000243986 | + | 5.65303e-5i | ||||
\(841\) | 1.84249e7 | 0.898285 | ||||||||
\(842\) | −386470. | −0.0187860 | ||||||||
\(843\) | 1.87667e7 | − | 4.34814e6i | 0.909533 | − | 0.210734i | ||||
\(844\) | −6.52877e6 | −0.315482 | ||||||||
\(845\) | −6508.87 | −0.000313591 | ||||||||
\(846\) | 848954. | − | 415713.i | 0.0407810 | − | 0.0199695i | ||||
\(847\) | − | 1.62261e7i | − | 0.777151i | ||||||
\(848\) | −4.15800e6 | −0.198561 | ||||||||
\(849\) | 7.54223e6 | + | 3.25524e7i | 0.359113 | + | 1.54994i | ||||
\(850\) | − | 2.20994e7i | − | 1.04914i | ||||||
\(851\) | 3.72200e6 | + | 2.13873e6i | 0.176178 | + | 0.101235i | ||||
\(852\) | −2.49149e6 | − | 1.07533e7i | −0.117587 | − | 0.507509i | ||||
\(853\) | −1.89532e7 | −0.891888 | −0.445944 | − | 0.895061i | \(-0.647132\pi\) | ||||
−0.445944 | + | 0.895061i | \(0.647132\pi\) | |||||||
\(854\) | 2.12479e7i | 0.996946i | ||||||||
\(855\) | −1148.32 | − | 2345.06i | −5.37215e−5 | − | 0.000109708i | ||||
\(856\) | − | 5.48955e6i | − | 0.256066i | ||||||
\(857\) | 3.22040e7i | 1.49781i | 0.662676 | + | 0.748906i | \(0.269421\pi\) | ||||
−0.662676 | + | 0.748906i | \(0.730579\pi\) | |||||||
\(858\) | 3.01085e6 | + | 1.29949e7i | 0.139628 | + | 0.602636i | ||||
\(859\) | −1.79382e7 | −0.829462 | −0.414731 | − | 0.909944i | \(-0.636124\pi\) | ||||
−0.414731 | + | 0.909944i | \(0.636124\pi\) | |||||||
\(860\) | − | 11221.2i | − | 0.000517362i | ||||||
\(861\) | 2.92035e7 | − | 6.76630e6i | 1.34254 | − | 0.311060i | ||||
\(862\) | − | 1.09686e7i | − | 0.502786i | ||||||
\(863\) | − | 1.17289e7i | − | 0.536083i | −0.963407 | − | 0.268041i | \(-0.913624\pi\) | ||
0.963407 | − | 0.268041i | \(-0.0863764\pi\) | |||||||
\(864\) | 2.44816e6 | + | 3.00872e6i | 0.111572 | + | 0.137119i | ||||
\(865\) | − | 16035.1i | − | 0.000728669i | ||||||
\(866\) | −3.00756e6 | −0.136276 | ||||||||
\(867\) | −2.59044e7 | + | 6.00193e6i | −1.17038 | + | 0.271171i | ||||
\(868\) | − | 2.21013e7i | − | 0.995676i | ||||||
\(869\) | − | 1.01158e7i | − | 0.454414i | ||||||
\(870\) | 2878.15 | − | 666.853i | 0.000128919 | − | 2.98698e-5i | ||||
\(871\) | 2.75368e7i | 1.22990i | ||||||||
\(872\) | −1.13404e7 | −0.505052 | ||||||||
\(873\) | −1.34805e7 | − | 2.75294e7i | −0.598646 | − | 1.22253i | ||||
\(874\) | −1.65618e6 | + | 2.88221e6i | −0.0733378 | + | 0.127628i | ||||
\(875\) | 32085.9i | 0.00141675i | ||||||||
\(876\) | −8.93421e6 | + | 2.07001e6i | −0.393365 | + | 0.0911407i | ||||
\(877\) | −2.08107e7 | −0.913665 | −0.456833 | − | 0.889553i | \(-0.651016\pi\) | ||||
−0.456833 | + | 0.889553i | \(0.651016\pi\) | |||||||
\(878\) | − | 2.57686e7i | − | 1.12812i | ||||||
\(879\) | −3.73816e7 | + | 8.66113e6i | −1.63187 | + | 0.378096i | ||||
\(880\) | 4320.76 | 0.000188085 | ||||||||
\(881\) | 1.11999e6 | 0.0486154 | 0.0243077 | − | 0.999705i | \(-0.492262\pi\) | ||||
0.0243077 | + | 0.999705i | \(0.492262\pi\) | |||||||
\(882\) | 3.28531e6 | + | 6.70915e6i | 0.142202 | + | 0.290399i | ||||
\(883\) | 1.80864e7 | 0.780640 | 0.390320 | − | 0.920679i | \(-0.372364\pi\) | ||||
0.390320 | + | 0.920679i | \(0.372364\pi\) | |||||||
\(884\) | 1.17612e7 | 0.506199 | ||||||||
\(885\) | 910.133 | + | 3928.15i | 3.90613e−5 | + | 0.000168589i | ||||
\(886\) | 2.33164e7 | 0.997877 | ||||||||
\(887\) | − | 47004.2i | − | 0.00200598i | −0.999999 | − | 0.00100299i | \(-0.999681\pi\) | ||
0.999999 | − | 0.00100299i | \(-0.000319262\pi\) | |||||||
\(888\) | 1.64453e6 | − | 381029.i | 0.0699856 | − | 0.0162153i | ||||
\(889\) | 949342.i | 0.0402873i | ||||||||
\(890\) | 15289.2i | 0.000647009i | ||||||||
\(891\) | 1.86297e7 | − | 2.39999e7i | 0.786163 | − | 1.01278i | ||||
\(892\) | −1.55707e7 | −0.655231 | ||||||||
\(893\) | 318562. | 0.0133680 | ||||||||
\(894\) | 1.89883e6 | + | 8.19539e6i | 0.0794588 | + | 0.342946i | ||||
\(895\) | − | 479.052i | − | 1.99906e-5i | ||||||
\(896\) | 2.56411e6 | 0.106701 | ||||||||
\(897\) | −4.76291e6 | + | 1.57382e7i | −0.197647 | + | 0.653092i | ||||
\(898\) | −1.23343e7 | −0.510414 | ||||||||
\(899\) | 1.27488e7i | 0.526100i | ||||||||
\(900\) | 1.09120e7 | − | 5.34334e6i | 0.449052 | − | 0.219891i | ||||
\(901\) | 2.87154e7 | 1.17843 | ||||||||
\(902\) | −2.52891e7 | −1.03494 | ||||||||
\(903\) | −5.08123e7 | + | 1.17729e7i | −2.07372 | + | 0.480469i | ||||
\(904\) | 1.60235e7i | 0.652133i | ||||||||
\(905\) | − | 18317.7i | − | 0.000743446i | ||||||
\(906\) | −6.99789e6 | − | 3.02030e7i | −0.283235 | − | 1.22245i | ||||
\(907\) | 4.52552e7i | 1.82663i | 0.407256 | + | 0.913314i | \(0.366486\pi\) | ||||
−0.407256 | + | 0.913314i | \(0.633514\pi\) | |||||||
\(908\) | −1.31140e7 | −0.527863 | ||||||||
\(909\) | −1.40371e7 | − | 2.86660e7i | −0.563466 | − | 1.15069i | ||||
\(910\) | −8538.01 | −0.000341785 | ||||||||
\(911\) | 4.14032e7 | 1.65287 | 0.826434 | − | 0.563033i | \(-0.190366\pi\) | ||||
0.826434 | + | 0.563033i | \(0.190366\pi\) | |||||||
\(912\) | 295058. | + | 1.27348e6i | 0.0117468 | + | 0.0506995i | ||||
\(913\) | −3.35834e7 | −1.33336 | ||||||||
\(914\) | 7.53626e6 | 0.298394 | ||||||||
\(915\) | 3917.62 | + | 16908.5i | 0.000154692 | + | 0.000667656i | ||||
\(916\) | 1.01433e7i | 0.399430i | ||||||||
\(917\) | 3.16073e6 | 0.124127 | ||||||||
\(918\) | −1.69072e7 | − | 2.07784e7i | −0.662162 | − | 0.813777i | ||||
\(919\) | − | 4.19178e6i | − | 0.163723i | −0.996644 | − | 0.0818615i | \(-0.973913\pi\) | ||
0.996644 | − | 0.0818615i | \(-0.0260865\pi\) | |||||||
\(920\) | 4618.07 | + | 2653.63i | 0.000179883 | + | 0.000103365i | ||||
\(921\) | −9.11844e6 | + | 2.11269e6i | −0.354219 | + | 0.0820706i | ||||
\(922\) | 1.10757e6 | 0.0429087 | ||||||||
\(923\) | − | 1.84008e7i | − | 0.710940i | ||||||
\(924\) | −4.53319e6 | − | 1.95654e7i | −0.174672 | − | 0.753890i | ||||
\(925\) | − | 5.28765e6i | − | 0.203193i | ||||||
\(926\) | 9.59155e6i | 0.367588i | ||||||||
\(927\) | 6.55364e6 | + | 1.33836e7i | 0.250486 | + | 0.511533i | ||||
\(928\) | −1.47907e6 | −0.0563790 | ||||||||
\(929\) | − | 4.58157e7i | − | 1.74171i | −0.491542 | − | 0.870854i | \(-0.663566\pi\) | ||
0.491542 | − | 0.870854i | \(-0.336434\pi\) | |||||||
\(930\) | −4074.95 | − | 17587.6i | −0.000154495 | − | 0.000666805i | ||||
\(931\) | 2.51754e6i | 0.0951925i | ||||||||
\(932\) | − | 2.09344e7i | − | 0.789442i | ||||||
\(933\) | 1.08790e7 | + | 4.69539e7i | 0.409152 | + | 1.76591i | ||||
\(934\) | 4.65374e6i | 0.174556i | ||||||||
\(935\) | −29839.4 | −0.00111625 | ||||||||
\(936\) | 2.84371e6 | + | 5.80732e6i | 0.106095 | + | 0.216664i | ||||
\(937\) | 2.80439e7i | 1.04349i | 0.853101 | + | 0.521746i | \(0.174719\pi\) | ||||
−0.853101 | + | 0.521746i | \(0.825281\pi\) | |||||||
\(938\) | − | 4.14599e7i | − | 1.53859i | ||||||
\(939\) | −2.96366e6 | − | 1.27912e7i | −0.109689 | − | 0.473422i | ||||
\(940\) | − | 510.421i | − | 1.88412e-5i | ||||||
\(941\) | 1.71431e6 | 0.0631124 | 0.0315562 | − | 0.999502i | \(-0.489954\pi\) | ||||
0.0315562 | + | 0.999502i | \(0.489954\pi\) | |||||||
\(942\) | −2.47683e7 | + | 5.73868e6i | −0.909429 | + | 0.210710i | ||||
\(943\) | −2.70292e7 | − | 1.55315e7i | −0.989815 | − | 0.568767i | ||||
\(944\) | − | 2.01866e6i | − | 0.0737280i | ||||||
\(945\) | 12273.7 | + | 15084.0i | 0.000447091 | + | 0.000549461i | ||||
\(946\) | 4.40014e7 | 1.59859 | ||||||||
\(947\) | − | 2.46149e7i | − | 0.891915i | −0.895054 | − | 0.445958i | \(-0.852863\pi\) | ||
0.895054 | − | 0.445958i | \(-0.147137\pi\) | |||||||
\(948\) | −1.10683e6 | − | 4.77712e6i | −0.0400002 | − | 0.172642i | ||||
\(949\) | −1.52880e7 | −0.551042 | ||||||||
\(950\) | 4.09461e6 | 0.147199 | ||||||||
\(951\) | 1.08037e7 | + | 4.66289e7i | 0.387365 | + | 1.67188i | ||||
\(952\) | −1.77079e7 | −0.633249 | ||||||||
\(953\) | −4.27314e7 | −1.52410 | −0.762052 | − | 0.647516i | \(-0.775808\pi\) | ||||
−0.762052 | + | 0.647516i | \(0.775808\pi\) | |||||||
\(954\) | 6.94300e6 | + | 1.41787e7i | 0.246988 | + | 0.504391i | ||||
\(955\) | 341.331 | 1.21106e−5 | ||||||||
\(956\) | − | 6.45642e6i | − | 0.228479i | ||||||
\(957\) | 2.61490e6 | + | 1.12860e7i | 0.0922944 | + | 0.398344i | ||||
\(958\) | − | 9.53864e6i | − | 0.335794i | ||||||
\(959\) | 6.90812e6i | 0.242557i | ||||||||
\(960\) | 2040.45 | − | 472.762i | 7.14575e−5 | − | 1.65563e-5i | ||||
\(961\) | 4.92750e7 | 1.72115 | ||||||||
\(962\) | 2.81407e6 | 0.0980387 | ||||||||
\(963\) | −1.87193e7 | + | 9.16641e6i | −0.650465 | + | 0.318518i | ||||
\(964\) | 1.01631e6i | 0.0352235i | ||||||||
\(965\) | −9865.16 | −0.000341025 | ||||||||
\(966\) | 7.17112e6 | − | 2.36957e7i | 0.247254 | − | 0.817010i | ||||
\(967\) | 7.40403e6 | 0.254626 | 0.127313 | − | 0.991863i | \(-0.459365\pi\) | ||||
0.127313 | + | 0.991863i | \(0.459365\pi\) | |||||||
\(968\) | 6.63555e6i | 0.227609i | ||||||||
\(969\) | −2.03769e6 | − | 8.79471e6i | −0.0697153 | − | 0.300893i | ||||
\(970\) | −16551.6 | −0.000564822 | ||||||||
\(971\) | −4.58980e7 | −1.56223 | −0.781117 | − | 0.624385i | \(-0.785350\pi\) | ||||
−0.781117 | + | 0.624385i | \(0.785350\pi\) | |||||||
\(972\) | 6.17179e6 | − | 1.33722e7i | 0.209530 | − | 0.453979i | ||||
\(973\) | − | 6.21819e6i | − | 0.210563i | ||||||
\(974\) | 4.55002e6i | 0.153679i | ||||||||
\(975\) | 1.97315e7 | − | 4.57169e6i | 0.664735 | − | 0.154016i | ||||
\(976\) | − | 8.68919e6i | − | 0.291981i | ||||||
\(977\) | 2.13083e6 | 0.0714187 | 0.0357093 | − | 0.999362i | \(-0.488631\pi\) | ||||
0.0357093 | + | 0.999362i | \(0.488631\pi\) | |||||||
\(978\) | −2.37398e6 | − | 1.02461e7i | −0.0793650 | − | 0.342541i | ||||
\(979\) | −5.99529e7 | −1.99919 | ||||||||
\(980\) | 4033.77 | 0.000134167 | ||||||||
\(981\) | 1.89361e7 | + | 3.86706e7i | 0.628229 | + | 1.28295i | ||||
\(982\) | 5.65072e6 | 0.186993 | ||||||||
\(983\) | −4.68620e7 | −1.54681 | −0.773404 | − | 0.633913i | \(-0.781448\pi\) | ||||
−0.773404 | + | 0.633913i | \(0.781448\pi\) | |||||||
\(984\) | −1.19426e7 | + | 2.76703e6i | −0.393197 | + | 0.0911018i | ||||
\(985\) | − | 19352.7i | − | 0.000635552i | ||||||
\(986\) | 1.02145e7 | 0.334600 | ||||||||
\(987\) | −2.31130e6 | + | 535516.i | −0.0755202 | + | 0.0174976i | ||||
\(988\) | 2.17914e6i | 0.0710220i | ||||||||
\(989\) | 4.70291e7 | + | 2.70238e7i | 1.52889 | + | 0.878529i | ||||
\(990\) | −7214.78 | − | 14733.8i | −0.000233957 | − | 0.000477778i | ||||
\(991\) | 2.45529e7 | 0.794180 | 0.397090 | − | 0.917780i | \(-0.370020\pi\) | ||||
0.397090 | + | 0.917780i | \(0.370020\pi\) | |||||||
\(992\) | 9.03817e6i | 0.291609i | ||||||||
\(993\) | −2.58619e7 | + | 5.99207e6i | −0.832314 | + | 0.192843i | ||||
\(994\) | 2.77046e7i | 0.889376i | ||||||||
\(995\) | − | 2550.29i | − | 8.16641e-5i | ||||||
\(996\) | −1.58595e7 | + | 3.67457e6i | −0.506573 | + | 0.117370i | ||||
\(997\) | −5.51484e7 | −1.75710 | −0.878548 | − | 0.477655i | \(-0.841487\pi\) | ||||
−0.878548 | + | 0.477655i | \(0.841487\pi\) | |||||||
\(998\) | − | 2.68800e7i | − | 0.854284i | ||||||
\(999\) | −4.04533e6 | − | 4.97159e6i | −0.128245 | − | 0.157609i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 138.6.d.a.137.10 | yes | 40 | |
3.2 | odd | 2 | inner | 138.6.d.a.137.11 | yes | 40 | |
23.22 | odd | 2 | inner | 138.6.d.a.137.9 | ✓ | 40 | |
69.68 | even | 2 | inner | 138.6.d.a.137.12 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.6.d.a.137.9 | ✓ | 40 | 23.22 | odd | 2 | inner | |
138.6.d.a.137.10 | yes | 40 | 1.1 | even | 1 | trivial | |
138.6.d.a.137.11 | yes | 40 | 3.2 | odd | 2 | inner | |
138.6.d.a.137.12 | yes | 40 | 69.68 | even | 2 | inner |